Some things that you might want to look at are:
1: SAMMI-Specs. for 7.62x51mm NATO Chambers vs. Commercial .308 Winchester Chambers. I think you will find out that the Military chambers are slightly larger.
2: When "sizing" rifle-brass (especially after being fired in a Military sized chamber........the area just above the extractor-groove will be larger. If your sizing-die will not bring this back down to SAMMI-Specs. Then you may want to look for a sizing-die that sizes this are of the cartridge-case back down to "factory-specs.".
3: Going back to that fired brass.........is this your fired brass or from a "bulk-dealer" in surplus 7.62x51mm brass fired from an M60 or m240 automatic weapon (?).......again, check the diameter of the fired case just above the extractor-groove before and after sizing. Sometimes you can "adjust" the height of the sizing-die....sometimes requires a different sizing-die or the trimming of the contact area between the die and shell-holder (** Remembering not to set back the location of the neck are of the case.). I believe that last resort would be to "adjust" the chamber......maybe just touching it with a 7.62x51mm chamber reamer. Remember.....dies and shell-holders are cheaper than "Barrels" and "Gunsmith's fitting-time.....
Note: We found a lot of the above out through trial-and-error from making "Blank" ammunition for reenactors/movie business for over 20-years and using a lot of fired cartridge-cases.......well over 1,000,000 made.
US Army, RETBlanksguy2001@outlook.com