Re: Get a GRIP! (on the bullet.... that is).
You really do need dies with an expander ball. You can still neck-size using an F/L die set by simply turning the die out some distance (t.b.d.). As your die currently only contacts the outside of the case, normal variations in wall thickness will translate into variable inside diameter measurements. The I.D. can be dealt with using a sizing die that incorporates an expander. As to overall wall thickness; you would need to neck turn the brass. Probably not necessary on a factory rifle. I do believe it is more effective in small bore rifles like yours. Only you could determine what is ultimately going to work for your setup.
Definitely acquire a sizing die that has an expander ball built into it. I like the RCBS "X" dies--they do a good job in the calibers I've used it in.
Life's too short to shoot an ugly gun.....