I think I've made my own position quite clear.
However, are you saying that it's impossible to take the standard system, transform geometry so the earth surface is flat, with light bending along the new geometry, and have that work?

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What I'm saying is, if you propose the "transverse equatorial aspect of the azimuthal equidistant projection" as your answer to why the Tropic of Capricorn and the Tropic of Cancer measure the same in circuмference, then you have to use the "transverse equatorial aspect of the azimuthal equidistant projection" to answer EVERY OTHER QUESTION about the earth's shape, as well. It is dishonest, fake and stupid to jump from one model to another depending on the question asked. And it is dishonest, fake and stupid to claim that you "don't have a model and don't need one" when it becomes impossible to use the same model to answer all the questions. 
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One model, in answer to every question: that's the impossible obstacle flat-earthers have to face, and they HATE it.
Therefore, flat-earthers hate the real world; it conflicts with their subjective fantasy world (which changes form to suit their whims).

FEers could just take the standard model and transform it to some particular FE map. Any particular map would work. But the transform would need to apply to all aspects geometry and physics - the FE explanations I have seen only go part way.

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Flat-earthdom syndromers don't have any "standard model." In fact, they complain that they don't need any model.
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Their method is always incomplete because the truth is one, and flat-earthdom syndrome is full of holes.

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Flat earthers could take the standard model of modern physics and transform it to any particular FE map they want.

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But then they'd have to AGREE on something, and that's not happening. 
They enjoy the confusion of disagreement WAY too much.