I've been watching this thread, but haven't commented because I have never really tried to blur the background and have no real-life advice. It is a nice effect though and I will practice.
I had some thoughts though. Maybe a little too much blur in your shots, especially the first shot, I think I see some up/down blur that does not look right. Jim's car shots look like a good amount of blur.
In general (again, I haven't done this, lol), I think you need to start out around the minimum recommended shutter speed for your focal length, 1/focal length. First goal is to get a reasonably sharp shot of your main subject considering that you are moving the camera following along. Too slow and your main subject will be too blurry.
Goal 2 is to blur the background. For this goal, too high of a shutter speed will freeze the background. Too slow and you risk unpleasant vertical blur. The speed needed will vary depending on focal length and how far away the background is. So my approach would be to take a few practice shots before the main subject arrives. Start at 1/focal length. Pan at an approximate speed and see what shutter speed gives the most pleasing blur to the background. I think you will end up with a shutter speed within 1 or 2 clicks either side of the minimum shutter speed for your focal length. That speed should be fine to freeze your main subject.
Again, I'm just thinking out loud here, I haven't tried this.
As a side note, you might have some fun with flash and rear curtain sync. Probably not good to flash cars or athletes, but you can get some neat effects with a slow shutter speed and and then freezing the subject with the flash.