You seem to have wasted a lot of time in this! I only have experience in Maya, but ive never had a problem like this. I'm sry if some of my ideas have been posted but im short on time and cant read the whole thread. -try freezing the transformations. when this is not done, at least in maya, weird stuff happens with the…
Did you place the cube on his head in Max? If you did so, this can be a wrong up vector problem too. At least the part about the position of the cube... I'd try it with an unsymmetrical object. That way, you can see if it only moves there or also has an awkward rotation applied. The final output should have +Y as the up…