When I look for a fault on anything, I always look at the most obvious / cheapest solution, because sometimes the solution is simple. I use a process of elimination and get the easy stuff out of the way first.
What makes you think its the gearbox?
What speed does the humming start and is it metallic sounding in any way?
My money is still on the tyres because I have had this noise before and it is quite a common problem. ( google humming tyres!) but of course, I'm a bloke so could be wrong!
Changing one tyre around to different wheels will not eliminate that tyre. You need to inspect the tyres for uneven wear then swap each one with a good one ( spare?)
Or, if the humming comes in at a lowish speed, can you get to a smooth grassy / sandy area that will let you do the same speed when you normally hear the humming.
If the hum goes, it could be the tyres, but I think you should check that first.
If the noise is still there, then look at uj"s, propshaft balance ( take one off and drive again using diff lock) Check it while driving in low range ( is it still a road speed hum?). Check all the wheel bearings.
Only when you have checked all these should you suspect the gearbox ( unless theres a real reason you suspected the gearbox all along.)
Try simple fixes first, you never know, it could just be something easy to sort out.