Thanks, guys. Interesting links.
My knee pains are now mostly gone. I think the exercises the PT gave me - mostly leg lifts in all directions (front, back, sides, in between) helped, as did his advice to try to use lateral support muscles like the obliques to pull muscle tension across the front of the kneecap, thereby forcing it to follow the groove it is supposed to be in. I think I also symmetrized the lateral support muscles somewhat - I think they were originally a bit shorter on the inside ("medial") of the leg, possibly due to skating. It took several years of exercising to get rid of the pain. Though, if I make the mistake (for me) of doing strength training (or running) on the same day as skating, or anything else that uses stretches, I still feel some pain in the knees during deep knee bends.
My main current other concern is still stretching the muscles that limit bending forwards, bending backwards, leg high front, side and back, and opening my hips, because I am substantially less flexible than most people all those places, and because muscle strains have been my most common injuries. I always mostly feel the stretch for all those things around the inside of my calves, extending a bit up and down from there, including near the groin. Bending my knees releases that tension - I can even do a fair Yoga "Child Pose" - but that isn't always practical. I looked at an anatomy book, and found that the "Psoas" was in that region - though it's hard to tell, because a lot of other muscles are too. The PT (a pricey sports PT/ATC with great references, including by people in the dance and skating communities) verified that my psoas were tight when I go into stretched positions - but said that a lot of the sub-surface muscles were tight too.
They keep changing their minds about static vs dynamic stretches, and when you do them. For my particular body, I find by experience that static stretches before exercise help prevent muscle strains.
I've tried a lot of ways of warming up before stretching. Even soaking in the whirlpool bath at the local pool. Then, I try to stretch by trying to push myself (even in the whirlpool) into the positions I want to reach, as far as I can. That helps a little - but not much. But I get even less flexible if I don't do it. I've been working hard on this flexibility issue for about 20 years. I've taken a lot of Stretch and Yoga classes, but they haven't helped all that much.
The right answer "should" be to stop trying to do sports that require stretching those parts of my body. Unfortunately, I'm stubborn.
Warming up the surrounding muscles sounds good - except I don't know that I am succeeding in using any of the surrounding deep muscles. Warming up the surface muscles is easy, because I can feel directly that they are being used. I'm not clear that the heat will percolate downwards enough.
The dance kinesiologist (used by a number of dance departments, including the University of Maryland, to teach courses aimed at reducing injury incidence) claimed that exercising the specific muscle(s) before stretching would help with stretches of those specific muscles, because those muscles would become warmer than the tissue around them. Of course that is particularly important to dancers, because they often have other muscles and ligaments that are too long, leading to dislocations and related injuries. (Not my problem.) So it is beneficial to only stretch the muscles that need to be stretched. She also claimed that raising the heart rate helps oxygenate the tissues that might need to be stretched, which she claimed makes them stretch better, with fewer injuries. (But - doesn't exercise exhaust the oxygen in the muscles you use?) Of course that was a few years ago, and may be out of date, and I don't know how extensive her medical background actually was. But the PT said it made sense.