The GM trans was a turbo hydramatic. I remember helping a DIY RR owner in the UK rebuild his over the web, when discussion groups were mailinglists on list servers. He had a 67 silver shadow, IIRC, so it must have been the TH400 (no th350 before 69). So, all I know is that they have a decent automatic transmission which I could help you rebuild. The rebuild kits are about $150 for a nice one.
I think the cars are pretty darn ugly. And you don't want to be caught driving yourself. Unless you hace a chauffeur, you just look silly. I guess it can work if you drive and the wife sits in the back.
George