I picked up the book from my mailbox today. And it is what I have been looking for. It offers simple exercises to improve knee functioning, based solely on the function itself, not on what caused the knee problem. The author is a physical therapist at a large hospital, with a great deal of experience. But he doesn't just go on experience. He cites many different studies on knee problems, including some very interesting ones on arthritis.
He says there are four basic knee functions: muscle strength, flexibility, nerve awareness (there's a word for it - it refers to our ability to sense what our knees are doing), and endurance. He discusses each in turn, then offers simple exercises that don't require special equipment or a gym or money.
I figured out rather quickly why my swimming has been helpful. I try to keep my knees straight while swimming - this helps both my quadriceps and my hamstrings. I also found why flexibility is such a big issue for me: permanent fluid in the knee. He says a teaspoonful of liquid in there can severely limit flexibility as well as muscle power. This is an issue I might raise with the doctor I have seen twice now, when I am there for some other reason. That is, I'd like to find either a safe anti-inflammatory or another way to decrease the fluid retention in there. It may require sucking it out with a needle. In the meantime I can do the exercises. I did both the muscle strengthening and the flexibility exercises today, in very little time.
What excites me about this is that I may be able to avoid knee surgery altogether but still gain knee function and reduce pain.