That's three three-output gearboxes. That's quite a lot of real estate to take up :S
Have you considered having two modes instead, with outriggers bound to the gearbox? I've said this idea somewhere up here a while back but I'll repeat it:
Front loader mode:
You could then have steering either as an independent function with a sixth motor to avoid issues with slack as you mentioned, or you could have it as a fourth function in the front loader mode. If you're worried about slack then you could also use actuator steering for greater precision. Good thing about this solution is that you consolidate the outriggers into the gearbox itself, rather than needing a whole other gearbox for them. You could gear down the rotary changeover catches so that when your outriggers are up the catches are in driving position, but when they're down the catches are in backhoe position. You might have some issues with immense torque acting on the gearbox but you can implement a linear clutch (god bless that piece holy shit it's fantastic) somewhere in the drivetrain.
Another good thing is that instead of having three separate three-output gearboxes, you'll have four two-output gearboxes, the complexity of which might be greatly reduced to give you a bit more space.