IMO not tightness as a cause but muscular weakness which causes tightness and soreness. Therefore stretching, while good, is not a cure but rather as you found, a palliative.

I got some PT for a rotator cuff impingement. The PT said my posture wasn't good enough. Think dropping your shoulder blades into your back pockets. On the bike too, straighten your back and drop your shoulder blades. Oddly enough, this did help with the impingement. Exercises too, of course. This shoulder blade advice is all through Core Advantage. I never got it through my head that this was supposed to be a permanent postural thing.

I think something like this might address your weakness in a balanced way . . .
At the gym my Fall upper body and pulling fundamentals day, 3 sets of 12:
Lat pulldowns
Machine rows
Shrugs
Biceps cable curls
Concentration curls

Superset:
Side dumbell raises
Front dumbell raises
Bent over dumbell raises

Seated unsupported dumbell presses
Back machine
Roman chair, legs bent

IMO never do crunches. All back and ab work with the back straight. I believe that's the thinking now.

IME standing takes leg strength and endurance, best developed by repeatedly forcing yourself to stand until your legs give out. Exactly right to practice it on the flat first. Start with a big gear and a low cadence of about 60.

Our 10-day backpacking trip sure increased Stoker's ability to stand. She went in with a 40 lb. pack, came out with 25. We did lots of climbing in the mountains. Ooooh, was that good for us. We went out just killer on the bike after a 1-day rest. You have mountains, must have trails?