I brought my shoulders and the X-rays to an orthopedic surgeon last Wednesday and he tells me it might be tendonitis. I still have more mobility and less pain than a rotator cuff tear would give me, and the gradual development of the pain points to a growing inflammation causing painful impingement.
A very long-needled syringe was then used to inject Triamcinolone acetonide directly into my right shoulder. In two weeks the joint should be unswollen enough that I can restart strengthening exercises and get more Triamcinolone in the other shoulder, without needing surgery or therapy. (Hopefully.)