Don't accept an "open-end" quote. Or you will be on the hook once they take it apart, and by that time there is nothing you can do but agree with whatever they want to charge you for the "Extra".
They should already have an idea about what's wrong with the tranny, but they just do not tell you and quote you low price until you are on the hook. Then the "extra" will kick in and give them space to play. Get the "worst case" quote.
I once had some problem with the tranny of my Accord. Visited 4 tranny shops. 3 of them said the tranny is "gone" and tried to scare the hell out of me. They quoted 2500 - 4000 to rebuild.
The 4th shop told me it's a famous problem for Accord and it's not the tranny itself. I ended up spent $35 to fix it.
Ask around and don't be scared to ask detailed questions. Remember it's you that hire the mechanics to work on your car. You have the right to evaluate them before you pay.
I have heard horror stories about AAMCO, but have no personal experience.
If you're in a well-populated area, suggest getting an Angie's List subscription and check for automatic transmission rebuild experiences. I've saved substantial on fence replacement, painting, and other services w/ Angies List. About $40/yr is what I recall.
2003 Acura MDX w/ Nav
2006 Acura TSX
2010 Acura TSX
1994 Honda Accord
See you down the ROW!