Somehow I've softlocked it! I was changing some controls as I fell into a spike pit, and Kit didn't die. I can't jump (I assume spikes aren't technically "ground"), so I can't get out, and there's no "reset the player character" button anywhere, so I'm stuck. Even turning on Double Jumps wouldn't get me out.
It was fun while it lasted.
Interestingly, the camera seems to think I'm grounded, but that the ground is on a nonexistent platform above me.