are you using a single turret head and reinserting your dies? or do you have caliber specific turret heads setup?
if you're doing the former, i suggest you attempt switching to the latter. They're only $12 or $15 each, definitely a worthwhile investment.
i had lee pro 1000's setup for pistol, and i had a bunch of different heads for them - one for each caliber. Once you get the dies locked in tight on the turret head they dont move with the lee rings in my experience. Likewise for the rifle dies i had with the lee quick change bushings. but once i had a die adjusted and firmly locked into a bushing, i never took it out.