Firstly, instead of importing push, pull, grab, etc to the movement engine, try importing just movement to fleshy's engine. Less things you need to work with then. Just looking at the runtime I can already see a lot of Object Order and Collision issues. The core mechanics (Pushing, Pulling, Movement (minus camera scrolling), Throwing) are not all that different between GBC and LttP styles. I highly suggest you look over the GBC+ engine for some organization ideas. Not only will it make your engine flow easier, it will also make things more organized and easier to find/squash bugs.
Things to look at:
-Use of collision masks
-Qualifiers to group several objects together (HUD)
-Animations and Movement Stoppers (See: GBC+ Lifting, the player can't control movement while Link is lifting something, this is how it is intended in the games too)