It's not really the 'transmission' that has 4 reverse and 1 forward, it is the 'differential' that has the ring gear flipped, so the engine and transmission are spinning correctly, but the diff makes the wheels go backwards. Of course, in this case, the transmission and differential are integrated, but conceptually they provide separate functions.
Interested to hear how this resolves, because I had always heard they just flipped the ring gear. Of course this was casual talk, I never had anyone with Collier's level of knowledge to point out this was not possible with a slight helical cut.