I understood that the overworld time progresses automatically. An alternative to that would be treating the time you gain from dungeons as a resource you spend on the overworld.
Each curio you interact with gains you time. Each combat finished gains you time. So the question would be, will I have my party do something potentially dangerous to gain time?
You know, risk vs reward
Then the usage of time is like the spending of currency. Numbers can be tweaked.
You know, use it or lose it.