Wow!! Lots of answers. Sorry I got so busy and couldn't see what advice I got. Let me read through and I'll get back to y'all.
OK, I'm in no way bashing CCI or any other primer. I really dont have much brand loyalty. These CCIs though are screwed up in some way though. I'll mix some when I'm home and see what they measure. The priming tool I'm using, as I said in the OP is just the RCBS hand priming tool, nothing fancy but it DOES work and I've not seen a need for anything else. I have right around 4 thousand rounds of 5.56 ammo that I have stashed that I primed with it , using cci primers by the way, and every piece of that brass had a crimp, which was removed. This is not to mention the thousands of rounds of 5.56 and 6.8 I primed, loaded and shot using the same priming tool. 9mm, 38spl, 357mag, 10mm and 44mag and spl rounds also all number in the thousands, again, all primed with the same cheapo priming tool. So the priming tool I own is not the problem, sorry CCI fans.
Brass? All different brands as well. Some new, some range brass. Also sated in OP is the fact that I did swage the pockets if the several types of brass I tried to prime with these particular CCI primers. The pockets were already clean, and when I say clean I mean clean. Also stated in the OP is the fact that I even tried reaming and dreaming the pockets of several different brands of brass and that the primers would still crush going in.
I have not tried the priming feature on my press but I definitely will.
I agree that those S&B cases have just about the tightest pockets of any brass brands I've lo loaded, great brass though. Their 6.8 brass is the best there is. Pistol brass I dont know but I do use it. I've never had an issue with WW brass, in fact it's some of my most used brass for pistol.