I'm not crazy about strap-on racks because I've heard too many horror stories from people who have had their rack come separated from their car on the highway. If you notice other people's strap-on racks during your daily travels, you will be surprised at the percentage that are held on by a thread and a prayer. I know several people who routinely transport their tandems this way, but it's certainly not for me.
I think that your Town & Country would make an ideal tandem hauler if you'd take out a seat or two.