This may not be a reasonable or fair thing top say; but I gave up on Besslers in the 60's when I printed (B&W) for a couple of fairly well known photojournalists in Chicago. This might have something to do w/ the fact that the main 4X5 enlarger I had used from the time I was 8yrs old was an Omega usually a II or 2. But @ ~ age 22, I found that I was constantly fighting the Besslers. I was constantly running in to the standards w/ the easel or they were doing some flaky thing that took way too much time to work around. When I finished their darkrooms sessions, I would be ready to scream. I now suspect that Bessler has improved their enlargers. I can see that the columns are more slanted to move the easel away from the columns base as the head is raised.
Having said all that, I tend to believe that many Bessler users of your model haven't had your problem. I find the angle / tension of the tension members very interesting, but have no idea if that has anything to do w/ U're problem. Having worked in machine shops, including in a nuclear reactors, worked on cars, built precision racing engines, worked on motor cycles, & bicycles, I have usually found that when a truly long term confounding problem appears, it's usually that I failed to figure out the exact operation of mechanism(s) behind it's operation, or that some structural part had partially of fully failed, & I couldn't see it. It could be due to ware of mechanical parts (too much slop) or distortion ( bending) of a structural part. Or just out & out unseen failure (cracking / tearing), softening of the part to do repeated loading. (Although that's supposed to, to work harden the metal) but it doesn't always go that way. There is usually something I didn't see until I let all preconceived ideas go of what the problem is. I have often gone to sleep asking relevant questions & bingo, the next morning the answer popped into my mind.

Now I have a probably unanswerable question: What are the most stable enlargers for holding alignment? I suspect Durst, (For the experience I’ve had w/ Dursts), I love them, but expense & difficultly getting parts here in the US eliminate them.
2. When aligning various brands/ models, which are the most reasonably easy to align & keep aligned? I suspect when all is said & done; Omega; but that may be my > 60 year predijust ;-/
Thank you for your thoughts, Jay Drew