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.
It still allows an infinite number of long rests with minimal effort - personally I wouldn't call that an inconvenience, more a nuisance/annoyance.
There needs to be some real restriction to doing that - maybe respawning (nameless) enemies so that you loose a chunk of process (this would also require removing EXP gain from these "respawns" to avoid grinding). Given that 5e is balanced around the idea of dungeon crawls, I think this would be the most logical solution, even if restrictive to progression, however, would at the same time allow a lot more engagement - opportunities to try out new strategies and such.
