I think the easiest solution to the resting problem that wouldn't require a major overhaul of the camping system is to have a waypoint at the campsite and make it so that you can only fast travel from a waypoint location. That way when you enter a new area, like when you fall into the Underdark, you can't return to camp until you find a Waypoint (or find a way to backtrack to one). It makes the most sense from a narrative perspective and limits how often you can camp. I'm also not a fan of how you can fast travel from anywhere on the map.
The only problem I could see is that it might make things TOO difficult. What happens if you fall into the Underdark and have to fight the minotaurs without any spell slots? I guess that's what fleeing from battle would be for.