Good Evening, Nathan,
The ordinary Beseler negative carriers are just simple, flat metal; any distortion or warping should be immediately obvious. As you have noted, 120 negatives can often show a bit of movement when in the carrier, but my experience has been that this is irrelevant. Once the negative is in place in the enlarger, there is nothing to move it, except for the remote possibility that heat from the lamp might cause it to "pop." That's something I've never seen happen with my Beseler equipment. I've quickly scanned the comments above and don't recall anyone's mentioning the possibility of enlarger misalignment, although that might well show up in prints from 35mm also.
Have you tried printing a different apertures to see if overall sharpness varies? If you're using ƒ8, you might try ƒ11 at twice the exposure time or ƒ16 at four times.