I went through Hive 3 again today, broke down a lot of queen cells, and got rid of several that were prematurely capped. If they're capped after four days, then they were raised from larvae which were too old to make good queens. I used to have a strain which never did this, so I have to assume it's genetic, and can potentially be bred out. In another week or so, when the bees have had time to build up and strengthen the cell walls, I'll split Hive 5 as well, and give a couple of cells to the queenless side. It's then a matter of waiting while they hatch, mate, and start laying.