It took me a few days to get back to this, but here is an update.
I removed and disassembled the FL Sizing die, and I cleaned it out with brake cleaner. Reassembled and set the decapping pin to protrude 3/16 inch. (Saw that on an RCBS Youtube channel video.) Installed and set up as normal. First problem I noticed: at least on my press (Lee Classic Turret) there is absolutely no possible way to install this die in such a way that the lock ring does not cover the vent hole. It just can't be done. Once installed properly, the vent hole is only one or two threads from the press. Once I tighten the lock ring, that' sit; it's covered. The only other option is to remove the lock ring.
Found some Hornady Unique paste type wax. (It was all that was available.) Used my fingers to apply a film to just the wall of the case and rim, no wax on the shoulder or above. Used twice fired, previously neck-sized only cases. No more screeching, chattering, or noise at all, no more dented cases. A little more force required than I would like, but otherwise, it worked. For about 10 cases. Then the denting came back. Very minor and only one or two at first. Now, big dents every single case.
So, I'm pretty frustrated. Also, I would like to point out that I FL size 30-06 cases on a Lee FL sizer for my M1 using RCBS Case Slick and have never had a problem at all. (I think that's why I was able to blast through 60 cases without even realizing I was wrecking the cases. I never even thought to look for dents.) But I've now damaged about 70 cases using a water soluble spray, two different aerosol lubes, and now a paste lube.
It has become obvious to me by now that these RCBS dies are complete garbage and are ruining my cases (this is the 2nd RCBS die I've used on this.) The only issue I had prior to this, when I was neck sizing only, was the cases were getting to the point that they would no longer load into my chamber. So, at this point, I'm done with this. I'm no longer going to FL size these .243 Win chases, and I'm going back to NO sizing. Enough is enough, and 70 cases is enough. Going forward, when I get a case that won't load, I will just consider it the end of life for that case and discard it. That's a lot easier than the time, money, and frustration I've had trying to FL size just to extend case life. I've spent days working on this, and now I'm against the wall with a match tomorrow morning and zero ammo loaded for it.