There are hundreds of small flight schools that offer low cost international students a chance to fast track their flight training. I personally don't know much about Cirrus Aviation in Sarasota, but I do know of good flight schools that are SEVIS approved in Gainesville and Ocala, Florida. I'm not sure if I'm aloud to disclose much more info than that on this site. PM me if you'd like a bit more info, or just look on a map and do some good old google research.
Also... I agree with you on being careful with the larger flight schools. I get to talk to a lot of foreign students and the high prices that they're paying are insane.
p.s. What rating are you looking to get?