Check in the POV section for Walt's papers. You will probably have to read the whole set. You need to be at the home page for BeeSource to find it.
It sounds to me as if you didn't get enough empty space above the brood nest. "Shotgun" backfilling may be an artifact of brood age -- the bees are filling in the empty cells as they appear. If you had a huge pollen flow this spring like most of us had, the brood pattern was a little crazy due to lots of pollen stored in the brood area, causing un-even pattern filling by the queen. Bees had to eat the pollen they stuffed in there before brood can be laid in a cell.
Try to accumulate enough drawn comb this year. One way to do that is to move one medium down underneath the deep once the weather warms up. The bees will fill it with pollen over the summer, then use that pollen to make winter bees, leaving the comb empty. That box then becomes your supply of empty comb in late winter, and you can use it to checkerboard the hive even when it's too cold to inspect. If there are adequate stores, the bees should all be in the deep, making it easy.
This has been a screwy year, I'm not surprised CBing didn't work for you this time. We are at least two, maybe three, weeks early -- strawberries are ripe at the U-Pick, and they usually come in at Memorial Day! You may have been a couple weeks late on getting the CBing done even though it was really too cold at the time.
I'm going to try a deep and two mediums for the brood nest on my splits this year and see what happens when I checkerboard in the spring next year.