Splitting an requeening question

Im California and when I split my hives last spring I put a queen cell in with 2 frames of bees, fed them sub and 1:1 syrup and what not. They were not very fast in building up as you could imagine. In talking to people the least amount they usually make splits with is 3 frames of bees. I made splits yesterday with Q cells and 4 frames of bees. These should be good to go for the winter.

As for introducing new queens, I would kill the old queen about 2 days before your new queens arrive. I would then place the caged queen in between two frames of brood where the nurse bees are more likely to care for her and accept her before she is released. And leave the cork in the cage hole for probably 3 days before removing it for the bees to release her. This will get approximately 6 days of getting acquainted with their new queen.

One thing I would do is call ad cancel half the queens, maybe order 5. If you ordered 11 you might end up spending more money for less production, put the extra money you save into pollen sub and sugar syrup to build those splits up!!

OK, I live in North Texas and deal with the same problems you do. This is some of the things I would do. First, I would requeen the nucs, so I wouldn't need to deal with very defensive bees as a full double deep. Get those nucs started with a good queen and those problems are solved. Also, keep checking those nucs on a weekly basis for about 6 weeks, and cut out all queen cells you find, and you will find several. If you don't keep an eye on them, they will requeen and kill your good queen.
On the double deeps, put a queen excluder in between the deeps, and check after a week, then you will know where the queen is. When your queens come in, take the box that the queen is in about 100 ft. away and wait at least an hour to let all flight bees go back to original hive location. After an hour, go in and it will be much easier to find that feral queen and kill her. Put hive back together and put in new queen the next day.
Do not kill any of your queens until the replacement queens are in hand. You never know what might happen to those queens in shipment.
Dealing with feral queens in most parts of Texas makes one question why we keep bees. However, by using a few logical techniques, it can be made a lot easier. I use a spray bottle of sugar water along with smoke. If no flow is on, I think the sugar water works better, sometimes.
You should be OK to split all your double deeps, if you have the queens and don't mind feeding. They will have plenty of time to build up before cooler weather.
If I can help you in any way, just ask and I, along with many others on this forum, will be more than happy to help, if possible.