Is expecting the player to keep track of some variables (like, on pen and paper) cheating/against the spirit of the jam?

Thinking of using the bit as a source of RNG + letting player know about events (like dying, finding something, etc.)

it'll be nice to hear what others think about this, but I think getting the player to track things is well well within the rules

This sounds like a wonderful excuse for 1-bit King's Quest.

I'd go as far as to say I think it's almost required! Especially for puzzley games. Having the player take notes or take time to reason about the bit isn't feedback; it's a form of gameplay and difficulty, basically. Sounds completely within not only the rules, but within the spirit of the jam itself.