Half twist! Very interesting. I think the length of the vbelt prevents the use of a twist? Would friction not be another issue with a twist?It looks like, from your picture of the motor, that there is a pulley on the motor, so that means there needs to be a belt also. Are you sure that the belt is put on correctly? Some machines with a Vbelt use a 'half twist' to reverse the final drive direction.
Also is this motor original to the machine, or is it a "refit", a different motor being put on the machine? I ask because you mentioned, "There is no other orientation that I can figure out to turn the motor 180 degrees to "mechanically" solve the issue."
This is the original motor. Not a refit.