Hi there, we have only done UK based back to back cruises, but hopefully the rules hold out where-ever you are.
In the days leading up to the end of the first cruise, we were contacted by the hotel desk to advis us that our cruise cards for the next cruise could be collected from themselves when convenient to us. One one cruise we also changed out stateroom, so the frontdesk made all the arrangements for our things to be moved for us. We didn't even have to pack, as a line of porters turned up, removed all the drawers & swapped them with those in the new room.
On the actual day itself, we simply used our new card to leave & rejoin the ship as if it were a normal port of call - well apart from we used the crew entrance, and of course the card was activated for use on the ship.
For the financial side of things, one line gave us a completed bill at the end of the first cruise, and we started again on the second. The other (albeit it a while back) simply rolled the first cruise's bill onto the second one.
Your best bet is to pop down to the front desk after a few days & ask them how they deal with the above - especially the room change if there is any.
Hopefully everything will flow as smoothly as our have,
Have a great time,
Alan & Katrina
Last Cruise: Queen Victoria January 2016
Next: Nothing booked
I have never had the pleasure to take a back to back cruise, but I see you have your question answered so I won't go into any explanations.
Having said that, however, I will say that I do not think that I am a candidate to experience such a vacation because: a)gaining weight eating all of that delicious food; b) have too many clothes to pack/wash/iron; c)if rough weather the entire time, would probably lose all that weight which I put on by becoming best friends with my head (toilet). Last but not least: can't think to spend that much time away from my fishies and kitties.