MHouser:
I get what you're doing & I believe the reasons for doing what you are doing (accuracy, right). It has NOTHING to do with cheap brass. You are simply trying to duplicate a tight neck custom chamber situation in a factory / standard chambered rifle.
I have done this in both 243 Winchester & 22-250 rifles, both using 308 Winchester brass & forming dies. I, however, was required to neck turn the brass in order to allow the cartridges to fire without experiencing a high pressure gas excursion.
Essentially what you want to check is that the outside measurement of your newly-formed brass, with a seated bulleted therein, measures LESS than your fired brass. IF it doesn't, turn your case necks. Don't forget about brass springback as well.
ALSO, make sure you start with starting loads, as the internal capacity may be less, especially if you are using old military 06 brass.
Smoke your cases with a candle & then insert them into your chamber & you may determine why you are experiencing hard bolt closure, with or without your bullet. I suspect it may be at the newly formed shoulder of the cartridge.
Have a look at the articles here:
http://varmintal.com/arelo.htm
Jim