Thanks for the feedback! I've been thinking about how being sent back is still making the search too long. I haven't yet tried limiting which rooms the missing members can appear in either, so I think that combined with staying in the same area is a good idea.
I'm also already planning on having the player be sent back to the inn if it gets too late. The health idea is good too! Since there's no battle mechanic right now, a game over likely won't make sense at this point.
If you're planning to add battles, you could just send the party back to the inn on defeat there too. I think that the kind of game you're making could work better by penalizing players with progress loss instead of having a full game over state. You'll just need to be a bit careful not to make the failure states unlock more events than actual progress to keep the players engaged.