I make plain base GCs from pop cans, using the Pat Marlin checkmaker. You need a dedicated checkmaker for plain base checks, caliber specific.
The 0.004in checks are swaged into the bullet base. This works best base-first. You could use a Lyman/RCBS lubesizer, or the NOE top-punch holder for the ram, in conjunction with a push-through sizer die.
The PBGC work well with lubed bullets. The increase the range of useful loads into the 16-1800fps, without any problems.
I've not, however, found these checks to make any difference with PC'ed bullets (in my limited testing).
The bullets below are some "seconds" from the excellent Arsenal 311-176, with PBGC- about to be tumble lubed. They shot quite well, despite having some defects. I'll soon shoot some more of those.