Hey again @AlphaNightFang! Just to get some clarification, when you say you're stuck, do you mean your adventuring pet is softlocked and needs to be moved?

Other than that, it sounds like you've reached the current stopping point in the main story. After beating the Haven Refuge plot, the mayor of Pixpet City asks you to go to the Arid Desert, and then it says "to be continued" (it's easy to miss though). There are still side quests you can do however, one of the biggest ones is in Homely Hamlet if you haven't already done it.

As for using a different adventurer, yes, you'd be starting from scratch. This may seem harsh, but it allows you to get adventure-exclusive items more than once.

Hope that answers your questions, and please let me know if I can be of further help!