I would first like to thank everybody that responded to my thread or private messaged me with helpful suggestions. This is a wonderful forum!
I purchased a small light table and compared a few negative frames I had made prints of from both 35mm and 6x7 formats. Both formats appeared identical in sharpness through a loupe. This told me that something was going on during the enlarging process. Long story short it appears that my Beseler medium format negative carrier is not pressing the negative down firmly like the 35mm carrier does. I'm not sure if one side is bent or the joint attaching each half is loose, but something is wrong with how it is holding the negative. I can push on the 6x7 negative and it will jiggle up and down very slightly. The 35mm negative will not move.
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.
We LF types control depth of field by things like swing and tilt. That's why we get far more in acute focus than people using conventional gear.
In a receding perspective, everything from your feet to infinity can be placed in correct focus. So it's actually a far easier problem with big view