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False shoulders are a bulge in the neck which serves to headspace against the chamber shoulder, created by expanding the neck with an oversized mandrel, then running the brass into the sizing die again to shrink the forward end of the neck sufficiently far enough to allow the case to chamber. This "wedges" the case between the bolt and the chamber shoulder, even through not all of the actual shoulder is supported. So when we fireform, the brass of the shoulder is blown out to fill the space. So for 30-06, needing to add ~8thou to the shoulder to avoid excessive case stretch, I'd anneal, pull up with a ~.323" mandrel, then run it back into the 30-06 FL sizer, setting the sizing die with the Bolt Close Method, sizing back the false shoulder JUST enough to allow the bolt to close.
Comparatively:
- CoW method wastes primers
- Bullet jam method has concerns for pressure, and if your application isn't one where jam is suitable, many folks aren't comfortable with the idea
- Hydroforming requires specialized dies and really begs for a press in an outside shop, or outside, since it's messy
But false shoulder method works with near-normal load data, precision will be nearly the same as the post-fire-formed result, and it doesn't require any special dies to accomplish.
(My preferred "next option" behind false shoulder, in the OP's shoes, would be bullet jam method. Seat the bullets long, jam hard into the lands, and use the bullet in the leade to create that "wedge" between the bolt face and the forward end of the chamber. I'd first prefer to pull a false shoulder to avoid the charge weight considerations of jamming, but my backup plan would be bullet jam. No sense in ordering custom hydroforming dies just to blow 30-06 out to a long chamber. I hate CoW fireforming).