When you FL size the brass and it fits tight, try turning the die in another 1/2 turn and see if it helps. Sometimes the "play" or slop in the press linkage will not allow the ram to run the brass deep enough into the die.

I always size one or two pieces and do a chamber check to make sure they fit ok.

Don't forget to put a little sizing lube on that brass, too.
If you don't you may become a member of the "can't get the brass outta the die" club. No membership dues and it's a lifetime membership...

PS - looking at the SAMMI size specs of brass for .270 & .300 WSM, there is a difference in the length from the case head to the top of the shoulder. The OAL is the same.

Look 'em up on a reloading data site and you'll see what I mean.