I have shot hundreds, getting close to a thousand 308 diameter 174 FMJBT's. These are hard military bullets. Not a problem in my K31's.
As long as the case neck can expand and release the bullet you won't have pressures issues when going from 0.307 bullets to 0.308.
Anytime the case neck is pinched, or the bullet is soldered into the case neck, then pressures can climb to extreme levels and blow the action.
This is what happened with the 1921 Tin Can ammunition. The bullets were coated with tin, the tin coating migrated into the brass case necks creating a “cold solder joint” between the bullet and case neck. This raised pressures disastrously and apparently caused blown rifles.
Instead of “fessing up”, the Army created a coverup, blamed civilian shooters and the grease they were putting on their bullets, and Hatcher supported the coverup 100% in his book.
However, if you have been shooting Swiss surplus, you might have noticed the grease ring around the bullet and the case neck:
I guess Hatcher lied!