There are a couple of possibilities. Most likely is that the way you are neck sizing is pulling the shoulder forward a bit. Are you using a FL die but only partially neck sizing? That will often do it, either as a result of the expander ball dragging the neck forward, without the shoulder being supported, or (depending on case shape) the die contacting the case body and squeezing it, again without the shoulder being supported.

I personally prefer Lee's collet dies, to avoid such problems. FWIW I only ever neck size.

Other possibilities (perhaps a bit less likely, but I've experienced these) include:

- your cases are seriously overlength, and are pushing into the leade;

- your seating die is adjusted down too far, so it is (excessively) roll-crimping the case mouth and causing it to bulge (this can also be a result of cases being over length, or of varying length - the over length ones get overcrimped);

- the chamber is loose, and when you fired the rounds they've bulged on one side, out of round, and won't fit back in the chamber properly if oriented any other way;

- your extractor has some fouling/damage/something stuck in it, so it is not able to slip over the case-head easily (a potential issue with Remington 700s in particular) or is not designed to slip over the case head;.

There are other possibilities too I guess, but I'd work through these first.

FWIW I do check loaded rounds through the action. Not always, but if I've changed anything or when they absolutely need to function. If you don't know how to do that safely you probably shouldn't have a firearm.