So I think I figured out what I have that is causing my tendinitis/tendinosis in multiple places, plus patellar dislocations - it's called Joint Hypermobility Syndrome (or, alternatively, Benign Joint Hypermobility Syndrome).

JHS is a genetic disorder affecting collagen production, and is thought to be a mild form of Ehlers-Danlos Syndrome Type III. It can result in multiple tendinitis/tendinosis, bursitis, sprains/dislocations, easy bruising, etc. Pain usually starts in childhood/adolescence but also can first be symptomatic in adulthood. It is apparently not that uncommon but underdiagnosed.

If this sounds like your symptoms, check it out. Here are a couple of links that I found useful. I apparently can't directly post links yet (being a new user) so sorry to have to write them out like this:

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