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the key with the new principal may be to allow ttwc to look the fool rather than you...you might want to accidentally bring this year's ap scores in, to show ttwc's weakness without being blatant.

talk with the new guy and be supportive of his work...offer to do some team teaching in the ap physics if possible?

as far as tap, it is really important not to have private meetings. anything you can do to find some good in the tap, please do so...any common ground at all will help minimize old hurts...go so far as to say something about the past and see if there is anything that you can honestly apologize for. if anything at all, she will likely take it to mean much more than it is, and perhaps work with you since you are asking her help...people like to be asked for help.