Before anyone jumps the gun; Yes, you could replace members generally by selecting the specified dungeon, and hitting "Join Party in Progress".

The question is why this doesn't work sometimes; I had a healer leave in my levelling roulette, and we waited for a good while trying to find a new one before disbanding it. I had requested in my FC (Others, Likewise) for someone to join it, but they couldn't find my party(And kept hitting a new one). Why is that? :/