character customization, link speaking, etc
That wouldn't be a Zelda game. A spin-off, possibly; Super Zelda RPG?
Choosing dungeon order is fine and good, although I wonder how you'd tackle designing the difficulty curve then. Come to think of it the first game had that, with no difficulty curve per se - you just went in and if it was too much to handle, ur fukd.
Consequences on HOW you beat a dungeon is asking for too much, and tbh it would be pretty annoying to have to do the same dungeon over several times, with minor differences, just to get to more story content. Consequences OF beating a dungeon would be cool though - like in OoT beating the adult dungeons had some effects on the world, I'd like to see more of that. Bring the land back from being a shitty hellhole to lush and full of life.