So there may be multiple reasons that this will not work, but what the heck: In the states there was a company putting out a rather sweet looking reversing diff called the Transworks mini-diff:



They stopped making it. I think that the reason was that it was primarily being sold to sandrail guys who are notoriously hard on diffs. Also, I think that the innards were mainly stolen from transaxles meant to go on aircooled veedubs. Not the toughest stuff around. Anyway....

What if someone were to take a common and inexpensive longitudinal transaxle, I'm thinking Subaru, but one could probably do the same with an Audi box as well. Cut off the bellhousing and unnecessary bits on the back. Modify the shifter shaft, install a new plate on the back, gut the innards, and boom! You get either a reversing box, or even a plus one forward gear to gain that precious low cruising RPM or higher max speed. Not the lightest, but in theory one could do a poor-mans Quaife:

You can get similar in the UK

http://eliteracingtransmissions.com/categories/motorbike-engined-sub-menu/mx200-il/

Muffet gears also used to make something a few years ago, price being the problem.