The M14 chamber is cut to 7.62NATO spec and not to the commercial 308Win spec. My USGI TRW M14 chamber would never have passed the 308 NOGO gauge, it measured 1.641. However, the 7.62NATO NOGO gauge allows up to 1.6445" and thus it was in spec. Since the op's M14 doesn't close on the 7.62NATO NOGO gauge, it is still in spec. The question is, is the measurement accurate without removing the extractor and ejector from the bolt? Below are measurements for 308 and 7.62 GO and NOGO gauges.
7.62 NATO GO Headspace Gage - length is 1.6355" plus .0003" minus zero
7.62 NATO NO GO Headspace Gage - length is 1.6455" plus Zero minus .0003"
.308 Win GO headspace Gage - length is 1.630" plus .0002" minus zero
.308 Win NO GO headspace Gage - length is 1.634" plus zero minus .0002"
.308 Win FIELD headspace Gage - length is 1.638" or 1.640" (?????)
Note that 308 NOGO gauge is smaller than the 7.62 NATO GO gauge!!
What we have here is a chamber close to max spec and steel cases. The M14 was never designed for steel cased ammo and I would never shoot steel cased ammo in the M14 unless I know it had a tight headspace. Anyway, just my $0.02.
Maybe 45ACPking and/or Tactical Teacher could chime in here and give us some of their M14 expertise here and put this puppy to bed?