Hello, I have no idea why it's a mess like this.

A temp "fix" is to export your model as .igs and reload it.
While the model will not be a solid anymore (they are a bunch of naked edges that I have no clue how to correct), at least you should get a better .FBX export when it comes to flipped surfaces.

An other oddity is that separate and rejoin all the surfaces in MoI also break the solid state (you end up with an joined srf model), but for some reason the "naked" script don't show any open edge :/.