The humming noise when you get on the gas sounds like it could be a bearing or possibly even a u-joint. A u-joint would be told by if you put the car in reverse, and when you first back-up, it feels like the drivetrain 'pops' loose from being binded up.
A bearing bad in the rear-end would be best solved by a rear-end rebuild kit. And if you haven't already, might as well do gears at the same time.
My car is making a similar noise, and I am wondering if I could be 'low' on fluid in the rear-end
But, since my piston rings are bad, I am not too worried about it
Just my 0.02