.
Two months later and still no answer.
Maybe because flat-earthdom syndromers don't have an answer!
This thread discusses one flat map, the transverse equatorial aspect of the azimuthal equidistant projection, that does have the same lengths for the tropics.
As given, however, that map would have problems with other things. Eclipses are not explained any better, nor that the same side of the moon is visible from everywhere on earth.
But one could take everything that works in the standard system and transform it to a flat earth, changing the geometry for physics as well (so light bends along the new geometry). Still observationally equivalent, right?