well until I see the mesh in question and found out how it's being exported we can't say.

personally I'm having zero issues with " triangles get messed up and overlap in unacceptable ways or the triangular planes intercept each other." here. how are you exporting out?

as an example of what I'm exporting out to poser see the attached image... - modeled in Sketchup 7, exported with a free Ruby to OBJ and rendered in Poser Pro. (textures by LaurieA) - a work in progress... I hate UVmapping....