Forwarding to next room would be the same as if autojoin tried to join a room that was full or locked, on peer connected (after game started) host can kick with the message current room name + 1, which the peer can use to retry joining again after getting kicked.
If you're not utilizing autojoin, that wouldn't work. In that case, I'm guessing you already have a lobby system where people can browse and pick rooms to join. Then the method of moving to a new room upon starting a game would be the most suitable, as you can then display only rooms that have space as options to join.