I think I finally fixed my vibration problem. Last weekend, I replaced the front pads, turned the rotors, cleaned and lubricated the caliper slide pins, put on new rear drums, new rear shoes, new rear wheel cylinders, and put on two new tires (on the front). Right now, the car probably drives as smooth as I could expect a 10 year old car with 134K to do.
I still don't know what was causing the problem. I've worked on that vibration problem for two years. I suspect the problem was either in the tires (one was slightly out of round (very slightly), or in the front rotors, or in the rear drum. When I opened up the right rear drum, I found a leaking wheel cylinder, which had caused the drum and shoe to be gummy, gunky, sticky. I figure it's possible that an intermittent drag from a sticky brake shoe might cause a vibration under certain conditions. Don't know.
Now, if I can just get the air out of the brakes, so I can stop the car without having to run into a tree, I'll be in business. I hope.