This is really satisfying in terms of the core mechanics. A couple of small points though:
- Could you mark the upgrade rooms on the 'map' at the top of the screen?
- The lack of healing is a bit punishing. +2 health is a bit too underpowered to take as an upgrade, but the effect of losing health ends up compounding as you try to reach the end, especially as in later levels a mistake generally ends up costing multiple HP. Even if you don't want to fully heal the player, I wonder if there's some sort of trade-off you can offer to players who want to get some health back?