Wel that's the real trick, isn't it? There is no proper way to model the Moon in FET.
Just because neither you nor I can come up with one doesn't mean it doesn't exist, and since the Earth is flat there must be a solution.
Hmmm, nobody in the entire history of civilisation has so far come up with a theory that fully describes every observation of the Moon - except for the simple one proposed by the round earthers - that the Moon is a large sphere, very far away, that orbits a spherical earth, which in turn orbits the Sun at an even greater distance. Funny how that one sentence there provides an explanation for phases, eclipses, libration, tides, appearance of features on the Moon - everything.
Saying "There must be a solution because the earth is flat" is circular logic. If there doesn't appear to be a solution in your scenario, then maybe there isn't one.