I personally have not had good experience with Aamco, they did a rebuild for one of my cars many years ago and botched the job bad. Pinched the seals, tranny had a hang up condition and performance of the transmission was very poor. I spent close to the same price you mentioned above as well.
I then spent $300 on a used transmission and stall converter combo with about 3k miles on it that was far better build then the Aamco build. That tranny lasted me the rest of the time I owned that car and many many trips to the track as well.
If you really found someone that could do the swap for relatively cheap money, then it might be a alternate option then spending close to $2000 on a rebuild. The place Blue recommended might be a much better option then AAmco too.