It sounds almost like you have the crimping die adjusted too tight and it is bulging the case. I crimp my .30-06 NEF rounds and they chamber fine.
Greybeard, it can make a difference in accuracy (or rather precision) with these little rifles if you crimp or not. They seem to have a long throat, and crimping helps with building up pressures reliably from shot to shot. However, the NEF (caveat: in my experience) is rather finicky on what it likes and the only way to find that out is to change variables when reloading. But only change one thing at a time, i.e. load up two batches of cartridges, same powder, same charge, same bullet, but crimp one batch and not the other. Then shoot them and see which gives a tighter group. But you know that already... :>)
-WH-