Great addition. I understand why there weren't multiple implementations in this demo, but the specifics of how you handle non-full-height jumps in particular often inform the rest of your jump physics. Meat Boy, I remember reading somewhere, actually goes one further than what you described and will invert your y-velocity when you release the jump button to prevent the top of your arc from feeling floaty (as opposed to increasing downward acceleration).
As to why directly physics-engine based platformers don't feel quite right, agree that it's pretty hard to pin down. My guess is that objects and the player receive the same gravity in a physics engine to keep things consistent, but a natural-looking gravity for objects is too floaty for players and good player gravity makes the objects feel like they're on Jupiter. I'd need to experiment more though.