AHHH, YES.. Now that I look at the photo, one can see the part/join line on the combing rail between the two rear wheels.. ( and the wheel nuts are in the same position)..
To be honest, you already have a strong transfer case that gives you 2wd/4wd.. So why not look at just building a power divider to attach to the rear of your existing transfer case.. reason being that you already have a live axle on the rear, so why not two. Something like my very basic sketch.
Also in a lot of cases, a lazy causes drag, (and therefore more fuel)..
The big problem as I see it is to get the rear (3rd) axle prop shaft past the 2nd axle... So, why not consider what Mack did with their Renault diffs and turn them 90 degrees so as the pinions face upwards?? This way you only need to run one prop shaft to the back and manufacture the necessary 90 degree inputs to the diffs plus a double universal shaft (jack shaft)with a slip yoke between the diffs..(a shaft like that could be easily picked up at a 4wd wreckers).. And if you wanted to get fancy, you could incorporate a remote controlled( air / electric\hydraulic/cable) splitter/disconnect in that shaft to isolate the rear axle..