Thanks very much Ristow! That makes sense with the wave ring. I may just get one, since I received the wrong reverse band and have to wait for that...
The steels were in great shape, so I did not buy new ones. In fact everything, except the one band, looks like new. I only saw one spot where a band lining piece was dragged against the drum on the way out. So I don't know what brand they are. All my new parts/gaskets are standard Pioneer, etc. Nothing special.