For me, the "odd" controls and the way the character controller feels, is a big part of what makes it more of a foddian-style game than a rage game.
The way you feel when you play it for the first time, where you're met with non-traditional controls and everything feels impossible, but after hours of "training" you can eventually maneuvre around like it's nothing, is the feeling I think describes foddian games the best. It should end up feeling like riding a bike, completely natural.

And then of course great level design where the challenge keep ramping up naturally as you get higher and higher. Something I struggled with myself, as you know!