Here is what I made when I didn't relube the 2nd time in the and pulled the head off the case.
It's a 7/16" X 20 tap and bolt to pull the case out of the die. The cup is machined to fit the die and center the pulling process.
Its very close to breaking through the case and into the die if not centered.
So I put it in a collet and hit the jagged edges with a boring bar to leave a clean start, use milling machine or lathe for best results, and tap with a centering bar engaged in tap. Works good, save your die.
I am a fan of Alpha brass, it works very well in normal loads and even pushed to the higher pressures it holds up in my 6 Dasher.
But when I want maximum velocity performance I use hybrid cases...they have preformed well in a variety of cartridges I use them in.
The maximum effort LA 8 twist 308 has shot 230 Atips to 2728 fps, 250 Atips to 2515 fps, 200 SMK to 2952 fps but accuracy was around 2900 fps for a .715 BC bullet out of a 308, and the new 177 SMK .545 BC to 3126 fps.
The problem is powder availability, and powders in general. The powders that boost the velocity are not generally available today...especially those from Alliant.
Other powders will work but are not able to get the velocity boost needed to justify doing the hybrid case, in many instances.
Varget is one, it's an accuracy powder, that through the yrs has had a lot of variation in burn rate, and slow velocities from lot to lot.
Shot Varget in my 16" auto with 168 gr and velocities were all over the place, S/ D was like 54 fps, the worst powder ever shot it that 16" AR rifle.
Change to a ball powder 1/2" accuracy and single digit S/Ds.
it is what it is....