I have not seen queen cells started before 20 hours, but dont have the experience Mike has for sure.
If there are eggs in the hive they may well start their own cells on their own eggs, so check the entire hive when you pull your cell bar out, you may find you have a couple extra cells elsewhere.
I have also pulled a cell bar out and found it empty, while there were a dozen queen cells started on their own eggs... So I will often pull the old queen and enough bees to make up a double nuc with her, and then wait 4 or five days, destroy the cells they started and insert the larvae I want them to use...
Like you said, I will pull one box off and condense the hive down to two boxes. If you put most of the eggs in the nuc and leave the capped brood in the hive and one frame in the nuc. It will help both get a good start. The extra box? Use it to make up the double nuc the old queen is going into. Eggs, a little capped brood, and some empty cells, both for storing resources and to give the old queen laying room..
You will find that its pretty easy after you have done it a couple times, and quite satisfying to raise your own queens.. There are many ways to make it work, so long as you just remember that the bees will do all the hard work, as long as you provide them with the right circumstances and resources.