[mindless]

Bob, I taught HS physics for 3 years (including AP physics) before I made a drastic career change, so I think I know what I'm talking about here.

Obviously, you're getting screwed here at some level. While teaching freshman is an interesting experience, you'd rather teach the more advanced classes with more mature students. My suggestions/thoughts:
1) Having students come in is a terrible idea. I think that it's unprofessional to bring in students to a teacher-related argument. No matter how well they say you taught, there's no way that the arbiter will say that you're more worthy of teaching an AP class.
2) The TTWC is a bit of a wild card, but reason with her at an emotional level to explain how you feel. She'll probably cry, but then maybe get your back.
3) (My actual suggestion) First, talk to TNG. Acknowledge that he was told he got to teach AP Physics, but ask if you can split the AP load since you did bring the class into the school. Offer him his pick of the B or C class, since maybe he prefers the calculus version to the survery version, which some teachers feel is less prestigious. Tell him that you'd like to sit down with him, and an arbiter to figure things out, but you'd much prefer to hash out a plan beforehand.
4) Where is the science department head in all of this? In the two schools I taught, the department head was in charge of the scheduling, not the AP.
5) If all else fails, can you get a promise to teach AP physics in the following year?