We have been on a few b2b cruises, and each one has been different.
Typically, this is what will happen:
All b2b passengers will be told to go to a particular gathering point (lounge, bar, etc.). After all other pax have departed, you will be given new SeaPass cards, escorted off the ship, through immigration, then back on the ship. Since you don't have the same cabin, you won't be able to go to your cabin until 1:00 p. m. (typically). By the way, you still have to pack everything the night before, but tell your cabin steward your new cabin assignment, and he/she should take care of moving your luggage.
Having said all that, I'll also tell you that on our last b2b, we were taken off the ship, and had to wait with the new group of pax until boarding time. We didn't have to go through check-in again (we already had our new SeaPass cards), but we still had to go through security.
It seems each ship has their own way of handling b2b pax. As far as I know, it has nothing to do with the port you are in.
Regarding any unused onboard credit......if you see you are going to have OBC left, you CANNOT transfer it to your next cruise. Use it, or lose it. I suggest you go to the casino cashier the last night out, and take an advance against your SeaPass card. They will charge you a 3% fee, but better to take the remaining cash than lose it.