Boomer, you asked: "After seating the bullet, can you turn it with your fingers?
Are you using a bullet with a very short bearing surface?
Have you turned or reamed your necks?"
I can answer all with a "No." I have an RCBS inside neck reamer setup which I have used when forming 25-06 from 30-06 and 270. This isn't the problem.
The rifle is fussy with OAL because of a longer than normal leade or throat. If I get everything right---which means seating no more than about .015 off the lands it shoots very well. Seat a hair too deep and groups open to 1.25" or 1.50".
I load 100gr Nosler Partitions and 100gr Hornadays, and they have a different ogive, and thus have to be seated to a different OAL. Adjusting the seater when changing from one bullet to the other is a pain, and if you don't get it right the first time things get worse because the conventional die deforms the soft nose automatically every time because that's where the seater plug bears.
I use the RCBS seater for Nosler and Lee for Hornadays now, and once they're set up it works fine, but I think it would be better if there was a seater plug available that was shaped to bear on the ogive rather than the tip of the bullet. This would also mean that switching to different weights would be a no-brainer. The drawing on the Wilson web site
looks like this is the case with their plug---but?
By the way, I've used brass brass

and nickel brass and RCBS sizing die and a Lee Collet die, and nothing works better or worse than another. Get the length right and all's well.