A Lyman M-die will greatly help this. It has an extended expander plug with tapered expanding wedge about 1/2" up the plug. You'll need to order the .311" expander. I use one in .309" for loading my .30/30 with .311" bullets.
Also, depending on the quality of your brass, you may need to neck turn the cases.
I've run into this with the .22Hornet case, which can be quite thin. Slight thickness differences in neck thickness cause the brass to stretch out in the thin areas when expanding the necks after sizing.
But, like the previous poster stated, the "easy and cheap" fix may just be to use a .310-.311" expander ball on the decapping pin.