You have been around a long time, tried everything and as weird as this is may sound I will state it anyway. For whatever reason, holding only a bar and using your BW to hang down and hold for extended periods has a way of healing shoulders. You have to have strong hands if you don't use straps, which I refuse to, and now I use the belt to put a few plates around my stomach (hanging down and use this as part of warm-up and shoulder injury prevention). I had two sore shoulders for months (years ago), physiotherapist was quick to diagnose it - I was sort of hunching over in my work chair and my chest muscles were getting stronger than the muscles that should naturally pull your shoulders back into a neutral position were not getting worked enough. No hangs though. I added those in everyday starting with 10 seconds and at the end I would just stop holding after 4-5 minutes. All the stability muscles around the spine, between my shoulder blades were not getting enough work so I had to do 4 'mobility/strengthening' exercises before every workout. I was better in a month. This is not your situation, but hanging by your BW has a way of somehow helping your shoulders healing and stretching everything out.
If you have a muscle tear or tendon/ligament tear this would be a big no, but for many joint issues/minor muscle imbalances this has a way of helping.
You no doubt know all this, but the other benefit is larger/stronger forearms/hands as given a month your grip will get stronger.