Bullets often have a pressure ring at the bottom of the bearing surface that's wider. Half a thousandth taper is common. Set the bullet sideways in a pair of caliper jaws and look for the light cracks to see.
QuickLOAD's drawing (often off by a thousandth) of the cartridge puts the bullet at .304" at the case mouth, but its database puts it at .306". The cartridge drawing on Wikipedia, taken from the CIP drawings, show the bullet at 7.78 mm (.3063"). But as with SAAMI practice, the given diameter of the bullet is a maximum with a minus tolerance. (For example, in .30-06 and .308", SAAMI gives the bullets as 0.309" -.003", but the chamber and barrel as .308" groove and .300" bore.) Thus I would expect the CIP bullet diameter to be on the large side of groove spec.
I ran into a description of the OP's loading issue with two K31's
in which the groove diameters slugged 0.305". Then the last post of this thread
says the CIP bore drawing dimensions are:
CIP bore diameter = 7.51 mm = 0.2957"
CIP groove diameter = 7.74 mm= 0.3047"
A look online for uploaded CIP drawings at Scribd
had one updated in '02 that agreed with the bore diameter above but gave a larger 7.77 mm (.3059") as the groove diameter for test barrels. The drawing looks official but is missing some tolerance information and gives the start of the rifling as a minimum groove diameter of just 7.70 mm (.3031"). So I don't know how far this drawing is to be trusted or if that's just what their tolerances allow?
Given the disagreeing information, but especially because the first linked to post reporting slugged two K31 barrels at 0.305", tending to validate the smaller groove diameter from the second thread link, it is reasonable to believe a rifle might have Ø0.305" groove a roughly Ø0.307" freebore, which would stop a .308 bullet from entering without a lot of pressure. (the Scribd drawing shows a 3 mm (0.118") long freebore, but gives it no diameter dimension). This is why I suggested the OP slug the chamber throat. Alternately, he could simply put magic marker all over his bullet and see what the contact marks looks like. If it looks like rifling marks, then it's just a very short throated barrel. If the mark is a ring, then he's hit the freebore and will need to narrow the bullets to achieve full 3.060" (77.7 mm) COL.