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Didn't bother to read past the OP, so it might be covered. One thing I know about new administrators (I used to teach, and my wife currently teaches) is that they have zero backbone with parents. Take up the students' offer and let the parents raise the hell.

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I think this is probably your best play. Multiple parents complaining will definitely get your opinion heard.

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the thing is, the kids who know i am a good teacher already had me and are gone, so they really have no incentive to do anything. i am not so well renowned as to have a following among parents whose kids have yet to have me.

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Really? No one who loved you when you taught regular physics and wants to make sure you’ll be there for the AP class? Or parents who have younger kids coming up in a year or two?

I can empathize with your situation as my Dad has had to deal with a couple strikingly similar situations the past few years. Populations can vary greatly but, at least at his school, some of the parents are fanatical about AP classes and, as has already been said, they can exert a lot of influence. I would think that getting a few parents on your side as well as emphasizing your past test scores will be your best bet.