It is often suggested that additional boxes be added after 70% of the frames have been drawn, though your weren't specific about all the frames, I'm assuming you meant they were all pretty well drawn. And yes, you now see why most people suggest uniform equipment, for ease of interchangeability.
Don't wait for the first sign of swarm cells before you prevent swarming, most of the time it will be too late. At the first sign of swarming, some keepers tear down all the queen cells they can find, and then open up the brood nest. Often times, the hive still swarms, leaving behind a queenless colony, sometimes there was still a hidden queen cell left intact. Either way, you lost half the colony, as well as a viable queen.