I am an AM student and have been for over 6 years. I have also taken lessons at independent studios. I don't understand why it has to be this whole "us or them" thing. AM and FADS offer different things than do the independent studios, but both hold thier place in the dance environment. I personally take lessons at a local independent studio so I get a slightly different perspective on what I am doing and us it as a supplemental experience to my dancing.
As for the cost, the independent studio charges only marginally less than my AM studio. And having said that, you only give up what you allow yourself to give up. I have only on a couple of occaisions paid my whole program in advance and I have NEVER paid more than I wanted to pay for any part of any program. I decide what is valuable and necessary to my dancing. Sales is part of what drives the dance lesson industry, even if it is an independent studio (they have to pay their overhead, too), however, if I am only comfortable buying 5 lessons, then that's what I buy. If I'm feeling more like I want to work on longer-term goals, then I may buy 30 lessons. Usually, I buy my lessons in smaller groups because I'm not in a hurry to get to whatever that ultimate point in dancing is. I believe it's about the journey of the art as it evolves in each person, not some final moment of completion.
Further, in MY experience, you get what you pay for. If you pay someone $50 a lesson, that's what you'll get and it may not take you very far down your path.
Don't pay the $6k. Have them break it down further. Ask what you can do with say 15 lessons instead of 45. If YOU aren't happy with what your teacher delivers, change teachers. If YOU aren't happy with AM, move on. If you are happy with your teacher and the environment, stay. Give it a chance, but be in control of your pocketbook. If you think AM is taking you for all you've got, then go to an independent, but don't think that just because they don't have a big franchise behind them that they can't rob you blind, too. That is for YOU to control, not your teacher or a franchisee.