Well, East Hill, I tried to do the spare tire trick, but it was heavier than I expected. Mounting it on the side made the bike want to twist and wobble crazily, and strapping it to the top deck felt top-heavy. That, plus having just changed a tire in the heat, helped me decide that it's okay for the car to carry its own parts.
However, last night I towed my son's bike about 4 miles to pick him up, and we rode home together. I'm sorry, my camera is MIA. I'll post some pictures when it turns up.