Measuring with what instrument? I suspect another person using a caliper
inappropriately.
This boolit diameter work requires a .0001 reading micrometer for accuracy or you
will make yourself crazy. Enco Tools online usually offers a decent Fowler mic for under
$40. Calipers are +/-.001 accuracy, can give .002 error easily and not appropriate for
boolit diameter work.

.306 will not work in .308 bore, you should have .310 to .311, but some succeed with
.309. First verify measurement accuracy, THEN deal with the issues. Seems unlikely
that a .310 marked Lyman die would actually be .306, not impossible but seem extremely
unlikely to have that much error.

Wait - I thought of something else that is possible. Some very old Lyman sizing dies have
a cutting shoulder and will literally cut a boolit if it is not centered perfectly. Newer ones
(for a very long time!) have a smooth, tapered entry into the die. Please look and see
if this has a step in the die. If so, you should polish out the step or much easier, replace
the die with a modern one. Theoretically, the step die can work, but it can also cut off
the side of a boolit and ruin it.

Bill