Alright, let's put everything down as one narrative we can copy into the wiki. I'll break it into sections again.
----------Chase--------------------
Link exits the Shiekah dungeon with the last cog finally in hand, only to find himself face to face with the aftermath of the Shiekah and Gerudo's battle. Seere, standing nearby, explains the situation to Link. "[whichever side you helped more] seems to have won. But both sides suffered heavy loss. We've lost too many warriors to hold the pass, but the Gerudo are retreating due to their casualties. I don't blame you for this, you just added a spark into years and years of kindling. In fact, I'm still not sure whether you're destroying Hyrule or bringing about the healing we've been needing for ages. But that's just me- there are some shiekah who definitely blame you for this. Oh! Here they are!" And several Shiekah warriors jump into the scene. The player is prompted to run.
Link scrambles across the rubble of the fortress, climbing collapsed walls and still-burning timbers to escape from his pursuit. He eventually loses them and returns to Hyrule castle to meet with his mentor and present the cogs.
----------Meeting with Ganon--------------------
The security measures at Hyrule castle have been increased multiple times to keep Link out, but he climbs and sneaks his way up to Ganon's quarters, finding the king waiting on the balcony. He turns and congratulates Link on collecting all the cogs, there is only one thing left to do before they can find the triforce and ruturn balance to Hyrule. But before Ganon can go on, a shiekah warrior jumps onto the roof, demanding the return of the cog before hyrule is destroyed. Ganon promptly refuses, saying it's time the triforce belonged to someone who'd use it, and attacks the shiekah.
Working with Ganon, Link takes the shiekah warrior down. Ganon raises his sword to deliver the final blow, but before he can end it, Zelda appears. "Well, Princess," Ganon growls, "it seems you've arrived just in time to discover that the once-loyal shiekah are now attacking allies of the royal family."
"Sheathe your sword, pretender" Zelda replies, turning to Link. "Link, I found a prisoner who had escaped from the dungeons lurking around the castle's library. He and a few friends want to talk to you." One by one, Link's gang arrives on the roof, followed by Farin. He apologizes for not being there for Link, but it's time Link found out the truth: Ganon isn't the Gerudo king, he hasn't even been seen by the Gerudo in 300 years. Ganon in an ancient villain who has returned to finally claim the triforce by manipulating all of us, including you, Link, and including me. Ganon framed me for murder seven years ago, forcing me to leave my people and abandon my throne. I am the true king of the Gerudo! Ganon is a villain who wants nothing more than the triforce, for his personal gain!
Ganon maintains his facade to the end, however. He brings up how he accepted Link when his gang spurned him, how he gave Link a purpose when before all Link did was steal from others for his own good. Together, they can still claim the triforce and save Hyrule. Link looks back and forth between each party. He eventually steps toward his gang. "Ah, so this is how it will be," Ganon says. "That's fine, you've been a weak pawn recently, wasting precious time to rescue the Zora royalty or cure the Gorons. If you'll allow me to take back what I've so graciously allowed you to use, I will bestow them on another pawn." Ganon uses magic to rip the cogs from Link and they float to him. "Thank you for your help, but only a fool holds onto tools after their usefulness is past"- and he pulls back his sword to attack Link.
Farin immediately jumps in front of Link, taking the blow. Ganon whirls back, laughing, then strides into the castle from the balcony. Zelda and the gang rush to Farin's side. Zelda inspects the wound and says that she'll have someone attend to him, and he'll be fine, Ganon was aiming much lower than your vital organs. Farin admits that's good news, however, Ganon escaped with the cogs.
The Shiekah suddenly warrior gets up from the corner where he'd been kneeling, surprising everyone who'd kind of forgotten about him. He says he knows where Ganon will head: He'll use the cogs to open the Celestial Clock, the vault that's housed the triforce since the last time Ganon tried to steal it. However, there's still hope- Ganon can't do it himself. Zelda agrees, saying she'd read about ancient magic that prevented anyone who'd ever touched the triforce from removing the cogs from their resting places. The Shiekah says Zelda is right- and the same spell prevents those people from entering the Celestial Clock. "Doubtless, Ganon's hatched some scheme to get in anyway," Farin interjects. "He must stop him." Zelda tells Link that she needs to get someone to attend to Farin (dude stop bleeding all over my castle), but Link needs to run ahead to try to stop whatever is happening, Ganon cannot get his hands on the triforce or Hyrule will be destroyed.
The player is now free to rush into the next dungeon, but all the gang members, Zelda and Farin can be spoken to. If you speak to Farin here, he'll mention some of his backstory- he was born as the King of the Gerudo, but before he came of age, Ganon framed him for murder. He escaped his execution with the help of a Gerudo witch named Syrup, but both had to split up and flee the desert. Farin was wounded during their escape, but he was found by a Shiekah hermit and nursed back to health, and he eventually tracked Ganon to Hyrule. He's been gathering information and waiting for the moment to expose the king. He should have told Link about all of this, he's so sorry.
Talking to Zelda will explain what's happened with the good guys since the beginning of the game. She apologizes for not trusting Link with her suspicions of Ganon, but to be fair, Link was working for him. She never fell for the bribes of treasure, stolen from Gerudo temples, that Ganon lavished on the royal family. And when she found one prisoner in the dungeons, Farin, who seemed to know that Ganon wasn't who he said he was, they started gathering information from within the castle. That's how they found out about the cogs and celestial clock, legends largely forgotten by the royal family.
The player should have had the option of interacting with the gang members already, so they just encourage Link.
----------Celestial Clock--------------------
Link runs to the entrance, only to find the cogs have already been placed into the door and the temple has already been entered. As he walks by the doors, he pulls the cogs out to continue to use their power (or maybe he doesn't. We'll have to decide, gameplay-wise, since we'll probably not want to rob the player of abilities they've been amassing right before their final battle.), and steps into the final dungeon, the Celestial Clock.
Inside, Link keeps catching glimpses of a mysterious figure ahead of him. Every time Link almost catches up to the figure, it sets off a trap to block Link.
Link finally catches up in a room empty except for a single sword enshrined in the center. The figure turns around and reveals himself as Sykes. "Surprised?" He asks Link. "I thought you'd understand. Back when everyone in the gang turned their back on you, you just found someone else. Well, the whole stupid gang decided that you're okay again, so they turned their back on me! But Lord Ganon saw that I was worthwhile. He's been training me to become a better apprentice, so I can finish the mission you couldn't! Want to try and stop me!?" With that, the temple's mini-boss battle against Sykes commences.
When Link wins, Sykes sits down and pouts. "All I ever wanted was to be accepted. I just want people to like me! And now look, everyone's turned against me, not even Lord Ganon would come into this maze with me. And I can't even pull that sword out of the pedestal!" Link walks up to the blade and gives it a tug. The room swirls around him and he is engulfed by a white light. In front of him, the Hero's spirit appears.
"Well, I guess it turns out you weren't so bad after all. I shouldn't have been so quick to judge you, after all, the blood that runs through my veins, the blood of the knights of Hyrule, also courses through yours. And that's why I'm here to help you. That sword- the master sword- can only be removed by true knights. The reason being that it's the final lock on the triforce, and also the pin that held together the spell keeping out anyone who's previously touched it. Ganon can now enter this temple- he's on his way here right now, but that's okay. With the spell lifted, I could get in here too. Ganon isn't the only one to step out of legend and back into Hyrule's fields. Accept the gift of the hero of time!"
And with that, Link and the hero merge. The white light fades, and Link swings the master sword. The really cool attack that the Hero has been shown to use is now available to Link, and will come in handy for the rest of the dungeon. The hero's voice echoes through the chamber- "Now claim the triforce for the side of light!" Link looks toward the door he didn't come through, which now opens. Naturally, he goes that way and gets through a couple more rooms to the end of the dungeon. (Sykes keeps sitting in the corner pouting about nobody liking him. You can try to talk to him, but he'll just snub you.)
Link reaches the end of the dungeon, but as he steps into the room at the heart of the clock, gears clicking all around, the face of the clock towering over him, Ganon steps in behind him. He thanks Link for helping him get this far, he really couldn't have done it alone, blast that ancient magic. "But I can see you're familiar with ancient things. You seem to have inherited the spirit of the hero of time. Once more our destinies cross." And with that, the showdown for the triforce begins.
----------The Final Battle and Conclusion----------------------
After a couple phases of the battle, Ganon will, typically, power up or something. Link doesn't know exactly what to do until Sykes shows up. He says that he's always been better at stuff then Link, so maybe Link could use some help. "After all, helping people... I guess that's why everyone likes you and not me, isn't it?" And the final phase of the battle is accomplished with Sykes' help.
The two outcasts defeat the king of thieves through their teamwork, and as Ganon collapses, Zelda, Farin, and the rest of the gang step in. Zelda, Farin, and Link form a triangle around Ganon's form. Zelda nods to Link and on her signal, the three of them do some magic thing that takes Ganon away. And at that moment, deafening chimes sound as the clock hands align at 12. The face or floor or something form a spiral staircase. Farin tells Link to go.
Link goes down the stairs to the chamber of the triforce. It hovers before him, shining and dramatic. So dramatic that there isn't even background music in here. The four cogs float away from Link and the shape of the Hero appears. He says "you won't be needing any of their magic anymore, I think you've proved that you're courageous enough to stand on your own. A true hero." He turns around and looks at the triforce. "Much bloodshed has come from coveting this, and if one who isn't pure gains it, more will follow. But you've never wanted more than to take care of your friends. It's a mixed-up world, and even I'm not sure who the bad guys are all the time. But it's said that if a person with an upright heart touches the triforce, his heart's wishes for peace will be granted." He turns back around. "So what will you do?" The hero walks to stand beside Link and stare at the thriforce. The screen fades out.
Then we get one of those ALTTP sequences of all the world's conflicts being resolved (implying that either Link wished had a righteous heart, or that he knew that people aren't all good or bad, including himself, and just trusted the good side of each person to work out their own issues. Magic or humanitarianism? Unresolved ending! Ambiguity!).
The deku get their king worked out, anybody else in the forest is doing good, the Zora royalty displays their bravery, the gorons bite rocks, Link's gang is dressed nicely and hanging out with Zelda in the castle, etc.. Everywhere, there is more equity and teamwork. The motif of disparity is resolved.
----------Epilogue--------------------
At the end, the game comes back to Link in a rebuilt section of the slums, and the player regains control (although he can't save, or leave this section of the slums). There is a mix of rich and poor people helping each other out, businesses are flourishing, there are plants and flowers growing, an old fountain that never worked is running again, etc.. People and different races from outside Hyrule town have journeyed here, too. Link will be able to find one or two people he helped out from different portions of the game. Some people the player can talk to have information about how the other places in Hyrule are doing: the shiekah left the fort destroyed so that the path to the desert is open, the shiekah and Gerudo realized after their huge battle that nothing good could come of their animosity, and they started working together to rebuild a joint Shiekah/Gerudo city.The Gorons have started their industry up again and have plenty of other people/races helping them, etc..
Link walks through all of this to come to the gang's hideout, which too, is fixed up. Inside, there's a small bakery in their kitchen that's giving out bread and soup to people, there's a library where a couple people are learning about stuff to better themselves and understand other cultures, and everybody in the gang is contributing to the community.
Link walks up to Farin, who's hanging out with younger children, telling them a story. He concludes by saying: "...the brave hero knew that the enemy was dangerous, but when he thought of all his friends, and how he would help them all if he could defeat the dragon, he gained strength. He beat the dragon, and if ran away, never to scare the village again. The end!" ...and the kids run off. Farin walks up to Link and tells him, "I've never been much of a story teller, I've never had time between worring about my people or trying to stop Ganon to be creative. But you know what? When I think of what you've done for everyone, selflessly helping out everyone in Hyrule, I get inspired. Link, I'm proud of you. You might have grown up a thief, and that's my fault. But you helped create a world where nobody has to steal anymore. You're a king among thieves."
THE END fades onto the screen, over a picture of Link and the gang waving goodbye to Farin from the city walls as he walks a packed horse toward the desert.
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Anything else to resolve?