Here's where I stand so far. Tdogg, I took your suggestion and reinstalled all the dies in the tool head, I made sure I was following the instructions in the Dillon setup paper exactly. I used a piece of Winchester brass for the die setup since that's what I have the most of.
I got everything adjusted so that first dummy would sit flush in the case gauge, so I then got two pieces of every other headstamp I have and loaded dummies with them.
Some brass did not want to sit flush in the gauge, but they were all from the same 3 headstamps. I feel pretty good about that because it suggests it's the brass and not my process at this point. Aguila, CBC and PPU did not want to work, but I was expecting Aguila and CBC not to, and I don't have enough PPU to really have any other evidence. Both pieces of it I tried didn't work so that doesn't make me feel too highly towards it.
Otherwise, around 7 other headstamps worked just fine.
I'm going to do the test again with different samples of the headstamps that work just to verify, but I'm feeling pretty confident at this point