Is it possible to grow a tamarind tree in a very large pot and prune it to keep it no more than 8 feet tall?

It'll be okay in a large pot for a while, even without pruning, and as its frost tender, it might be better anyway, so you can move it to a sheltered spot when necessary. It does eventually want to get 80 feet though, so I don't know how long or how well you'll be able to keep it going, but its worth a try.

Yes, I agree with Bamboo on this issue.