I think that any team without pneumatics who wants to make a transmission should minimize the amount of motors not directly powering the drive train. there are some 6-motor mecanum drives out there but they do not have shifting capability and do not use all of their motors under some operations. I am still working to get pictures of it on to the internet so i can link to them, but here is the basic premise on which it works. The motor powers the outside gear of a differential, with one of the two gears going to the sun gear of a planetary gear system and the other going to a shifting mechanism. The shifting mechanism is attached to the differential so that it and the planetary gear don’t have to turn together. Because the shifter is not controlled directly by the programming, it needs a way to discern if the drive train is under high stress or is being pushed backwards. To do this a rubber band is attached to the shifting mechanism so that the mechanism can only engage if the load on the wheel is greater than the tension of the rubber band. The entire gear system has two gear ratios, the first being a 1 to 2 for speed and the second being a 1 to .81 for strength. The fast ratio would be the default used for standard driving, and the gearbox achieves it by forcing the sun gear and the planet carrier to spin together and allowing the ring gear to spin freely. The strong ratio is achieved by releasing the sun gear and the planet carrier so they can spin at ration and locking the ring gear so that it cannot spin.
I remember discussing this a while ago in my CVT transmission thread with a member from 254D. It’s alittle different since it’s totally different transmissions, but I think the concept still applies in both.
https://vexforum.com/showthread.php?t=71209&page=3
I tried building something like this shortly, but it tends to be very touchy as many rubber bands don’t flex perfectly in sync. Also, with more powerful drive trains, the current differentials probably will break under the stress. I’ve seen (I believe it’s refereed to as a “Taiwan Drive”) a team use custom built differentials. I think if you wanted to build this system, it’s totally doable, but it’ll probably take a long time to perfect.
I hope that helps!
I did make on of these but I have not posted the picture yet. The differential would have to be custom made as you said, both because of the possibility of breaking and general warping. Similar to your transmission it would not be able to work backwards, but the solution is probably more simple. the biggest problem that my gearbox was having was the huge friction from all of the axles and gears, which would need a very sturdy frame to limit.
I uploaded the pictures and here are the links to the different views.
Top:
https://vexforum.com/gallery/showimage.php?i=5833&c=4
https://vexforum.com/gallery/showimage.php?i=5833&c=4
(The blue box is the input gear)
Closed (1 to 2):
https://vexforum.com/gallery/showimage.php?i=5830&c=4
https://vexforum.com/gallery/showimage.php?i=5830&c=4
Open (1 to .81):
I can not imagine putting two of these on one robot.
wow, thats BEAST!
@ andrew
ofc the “good copy” can be compressed by a lot
and college gets 24^3 this year 
Even then, its not worth the trouble. Believe me our bot will be quite something.
- Andrew
can you post a video?