Wow!
I tend not to believe in coincidences, either.
But to rule out the chance, would you try this?
Take two freshly fired cases. (Or, you could take two, new, never fired cases if you like.) After exiting your rifle, inspect the necks for scratches. Clean the brass thoroughly. If you have to, deburr the case mouths.
Clean the dies thoroughly, too. Take the depriming rod out and thoroughly clean the full length of the inside of the die.
Inspect the inside of the die as best you can with flashlight and magnifying glass or whatever you have.
Size one case in the Lee die and size the other case in the RCBS die. For simplicity (and to eliminate extraneous variables) do this without the depriming rod in the die.
Run a cotton swab (Q-tip) inside each die, looking for the brass "glitter" you mentioned. Examine the neck of each case for scratches and/or "glitter".
If you have scratches and glitter, I think you have two bad dies, from two reputable manufacturers (OK, for the Lee bashers, one reputable manufacturer and one "economy" manufacturer.
As Sherlock Holmes said in one of the Doyle's novels said, "Once you have eliminated the impossible, whatever remains, however improbable, must be true."
Actually the Holmes quote is an example of negative proof. What we have here is positive proof. The brass is unmarked when it goes into the die and scratched when it comes out. It's the die. Coincidence that it is both dies. (or maybe not, if both dies were damaged by the same cause, which we have not looked for, yet.) I reject the notion that it is misalignment of your ram. That could cause case crumpling or merely out-of-round brass, but not scratching. Besides, the same press does not damage your .308 brass.
Good luck.
Lost Sheep