Re: caged before the move!
I'm not sure I completely understand what you did. But, I'll try to answer. Yes, it is true that once they decide to swarm it is hard to stop them. Even if you knock all the swarm cells down they may still swarm. So splitting was a good move. But, it is normally better to move the old queen with a couple frames of bees into the split. This simulates a swarm and if you moved enough bees to releave the crowding it will help with swarming. Leave the swarm cells in the original hive so they will still have a queen.
If you moved your caged queen into another queenless split it should be fine as long as you go through a slow release to give the bees time to get use to her. Its the same anytime you move a queen into a hive with bees that are not use to her.