Have you tried 270 or 30-06 cases in your die? The qual-cart brass may be the problem ? ? Quality cartridge is nice because of the headstamp but "quality" for fit might not be there.
The 270 brass neck down may require two lube steps because of the "steeper" shoulder angle. Necking down for Ackley style cases can be tricky in the Ackley(gibbs) style die, but it should work providing the cases are not too soft.
Partial necking down in a 6.5-06 die may be a good first step to eliminate crushing.
My .02 with several Ackley' s of pain.