Thanks for the comments, all.
Sounds like my everyone likes the idea of leaving in the XP/levels. Like Rob said, I'll have to play with the tuning, I definitely don't want grinding to be necessary.
Right now, the only random drops are meat (hp restore) and arrows (once you have the bow, the way to get more arrows is by picking up drops). The idea of randomly dropping significant powerups sounds really tempting, but I'm not sure that it will work nicely into the system of persistent state that I've built so far. I'll have to think about it.
Right now, the direction I'll plan on going with it is that max HP is determined by your level and experience, and attack/defense is determined by which pre-set powerups you've found. But you never know, I may end up changing it after all.