Its going to be difficult to find a good vintage low A bari set up in good playing condition for $2000 or less. In fact, it will be difficult to find any bari in good playing condition for that price.
     The saxophone world is different than the trumpet world in that repairs are much more expensive. Saxophone have lots of moving parts and there are many way to damage them, especially baris. A full professional overhaul on a bari can run anywhere from $1000-$1500. So a lot of what you're paying for when buying a bari sax is the cost of getting it up and running. If you can stretch into the $3k price range, you'll have many more options available to you.
     That being said, look for Couf, King Tempo, SML, Welktlang, all as good affordable low A bari saxes. However, be wary of eBay or anytime buying a bari that has not gone through a competent shop. Some good saxophone dealers to consider are Saxquest, Tenor Madness, PM Woodwinds, and Sax Alley. Best of Luck!!!

Cheers,
     Mark Overton
     www.saxquest.com