I don't even own neck sizing dies and I reload most of my brass about 10X. Shoots pretty accurate too!
Shoot the brass about 3 times and "neck size only" with your FL dies. By that time the brass should be chambering real snug. Turn you FL dies 1/16 turn increments and size until it chambers with just the slightest bit of resistance. Works for me.
I can't get as many loading out of my 338 Lapua brass. 6 Loading and the paper clip tells me I can probably squeeze out another 1 or 2.