Raising your own queens is not out of the question. I just wouldn't recoomend the method you described. Your hives are in no current danger since they have queens and I assume are being productive. So other than dealing with them being mean in the interim, there is no reason not to give queen rearing a try. Here is a link to how I do it.Queen Rearing
Although I use the Nicot system, hand grafting can also be used. By using a couple of double screen boards, you don't have to dispose of your old queen until you are satisfied with your newly raised one. I like this, because queen rearing is by no means 100% and using this method, I am no worse off then when I started (can always fail back to original queen).