I have fired regular WWII 7.9 German ball through mine with no sign of excess pressure; the groove diameter slugs about .319". A .323" bullet is .005" oversize for a .318" groove diameter, not a big deal. The effect of an oversize bullet in raising pressure has been greatly exaggerated. At 40-50k psi, a bullet acts a bit like silly putty, pretty well shaping itself to whatever surrounds it.
There was some variation in those rifles and evidence that they gradually deepened the grooves over the years even before going to the new bullet, apparently trying to minimize wear even at the expense of accuracy or power. One report says that when converting those rifles they picked the ones with somewhat larger groove diameter, which makes sense.
The chamber neck diameter is more critical, which is why they ran a reamer into the chamber. If they had loaded the new round, with its larger bullet (and of course larger case neck) into the original chamber, the neck would not have had room to expand and the result would have been high pressure.