The issue with NCCS' companion scripts appears to have been resolved. The issue turned out to be that the newly-patched game engine handles the 'OnLoad' event differently than previous versions.
Since it wasn't registering the NPCs are having been re-loaded, the script wasn't updating correctly for newly-hired companions; and thus not correctly setting the variable that tracks whether the companion is merely "hired" or actually in your party. Since the in-the-party variable is what's checked to handle sneaking, weapon drawing, and similar functions, they weren't running.
I've changed when the variable is set in the new script version. It will now be re-set every frame, which should result in near-instantaneous updates to the companion's behavior.
I had been hoping to hold off on upload 0.6 until the new companion backpacks had a weight limit instituted, but I think this issue warrants a more immediate resolution. I still need to update the other nineteen companion scripts, and v0.6 should be going up to the Nexus later today.
I'd like to thank SuperSledgeNY for getting tired of waiting on me and taking it upon himself to track down exactly which function was causing the issue, and then letting me know about it so's I could go about fixing it. Thanks of course also go out to my ever-stalwart partner in crime, Herculine; for her tireless testing of attempted fixes (since I never did get the problem to manifest in my game).