So, when I didn't have the frame arm firmly pressing down on the top tube, there were considerable rocking by the bike on the rack. Mostly, fore and aft direction of the car, so toward the front and back. This seemed concerning to me for both the frame paint and the stability of the bike. So, I had been putting the extra effort to press down on the frame arm onto the top tube.
I think I like the foam tube idea. So, that might be what I will try to do when I get my bike back...