Sorry I'm late to the party!!!! - But yeah - What Dennis said!
We are all clay as well, about 50-80 feet down, the only thing that changes is the layers of color!
Yes, screenings are the best, also really help with the drainage around and under your pool, the more you can get the better - clay really soaks up moisture, primarily when it's wet season (makes sense right?) and then the winter freezes that and heaves it like crazy. I would recommend at least half a foot of the stuff under your walls for a width of about 3 feet (1.5 to either side of the wall) - then put your mason's sand in the inner circle and shape it like a saucer, you can probably get an extra 10 inches depth in the middle that way on a 33 foot pool, I got 8" and could have done more on a 30 footer.