I also accomplished this in my Spirit's Quest project. I'm pretty sure Diminish's is better (I haven't looked at it), but I do also have moving platforms and slopes and more advanced stuff like slopes that you can jump up through and land on, jump down from, etc. I released all of the data in my Spirit's Quest topic, but I've attached the editable of just the collision engine so you don't have to download the entire project. My code wasn't the most efficient, but everything works without flaw, and you should be able to look at it and see the general idea.
To give you an idea of what I did: I pretty much just had it loop according to the character's x and y speed and checked for collisions on each step of the loop. If the character collided with an object it would exit the loop. The slope code is in the loop of course, and it's a bit more complex than that with the solid and passable slope types, etc. If you look at it, you should understand what my idea was. There is also a slippery type in there, in case you might want to check that out.
Note: There are a lot of unnecessary calculations that come up because of the character design having a big head and small body collision. So you can pretty much ignore the "mask" changes and all of the "position correction" code. That code is separate from the x/y movement though (mostly).
I hope this is useful!