Just want to say that I absolutely loathe games with countdown timers, and really would like that to not be a feature in this one.

Would just rather you have to be in the overworld in order to rest, and if you're not then you can't. That's my suggestion. Thematically makes sense, and makes it so you have to commit for dungeons, or at least inconvenience you if you want to rest between every fight (requiring you to run all the way back through to get back from the overworld), which still thematically makes sense.