Supercub, if you can't get .311-.312 bullets the size and shape you like, you may want to try plain old .308 bullets that otherwise fit your likings.
I tried plain 180 grain Winchester PP's in two separate LE's and out to 200 meters (as far as I shot), I could not tell the difference between them and "real" .311 diameter Sierra ProHunter bullets. Groups were about 1.5" at 100 and around 3.5" at 200 meters, which were totally normal for those two rifles.
I used Lee 7.62 x 54R dies to neck size the necks to .308 without touching the shoulder or body of the brass. There are surely lots of other dies that would do the same thing...