OK, here goes. I believe the problem is essentially _insufficient_ agitation, perhaps with sliding reels contributing. So try this...(posted 8230 days ago)Load film onto only two reels and put them in the bottom of the tank. Put empty reels on top as "spacer" reels to prevent the loaded reels from sliding a lot. Once again, that's up to two reels loaded with film on the bottom and however many reels or combinations of reels on top.
Now..the important part...use _only just enough developer to cover the loaded reels_. No more. You want that big air space.
Pour in the developer, bang the tank a couple of times, then invert it _briskly_ at a rate of two to three inversions per five seconds for the initial 30 seconds of the development time. None of that "gentle" stuff. Then give it two to three inversions in five seconds every 30 seconds for the remainder of the development time.
Finish processing as normal although there's no need to use more of the other solutions than is needed to cover the film.
This may seem counterintuitive and illogical, while otoh perhaps millions of 120 rolls are developed yearly dip'n'dunk, which is pretty much the same thing, so rather than thinking yourself out of it just give it a try.
If this turns out to cure your edge-density problem you'll most likely find that your negs are contrastier and probably overall denser than normal; that's an indication that the agitation method that led to excess edge density was actually a case of weak, underdeveloped centers rather than excess edges.
This assumes steel reels, which I gather from your message you're using.
Some plastic reels somehow trap and hold developer in the image area that's underneath the plastic spiral with 120 film; these reels include the old Unicolor reels and the white Jobo 1500 reels. The only solution I ever found for the wavy line of edge density (usually only one edge) that actually mirrors the spiral was to use Jobo 2502 reels. Those reels have tiny molded nubs within the spiral that hold the film's surfaces away from the smooth spiral itself and permit the free flow of solutions all the way to the film edge.