I had this problem with an airvent in the past. For me it was not exactly z fighting. For example with my vent i had geometry for outside and inside of the airvent. Both 1 sides facing opposit directions. Though the vertices and polygons were in teh same position. Now theoretically the other side should be back faced cull but for wathever reason i got the black geometry you are experencing. To fix it i just selected all my verts and did a merge vert by a very low threshhold… then reexpor/ reimported it…for whatever reason it fixed the problem.