I've narrowed down the source of the problem to a single, simple change (however, said problem appears to be system-wide). Automatic weapons with their "ammo use" set to 0 instantly crash the game upon entering VATS. That's the only change that needs to be made to cause this "effect". If I were to guess, I'd wager that VATS is referencing this value somewhere as part of a formula. And while non-zero values don't cause any problems, zero obviously isn't quite as mathematically robust (particularly when it comes to division).

For reference, single-shot weapons do not cause this problem (pistols, rifles, grenade launchers, whatever) and can safely have this value set to zero without crashing. The problem is specifically tied only to weapons which fire in bursts when using VATS. However, I cannot comment as to where all this may be stemming from. I do have all the DLC and can't seem to turn them off to test this against the just base game (however, that shouldn't matter). I can and have tested unmodified base-game weapons against Gun Runner versions and produced the same results. The modified GRA automatic weapons instantly crash the game, while the unmodified base-game versions can be used freely.

I'm not honestly expecting a fix here (a little late in the game at this point, and far more important bugs to squash regardless), just making a note of said coding hiccup.