That is a pretty tricky repair to make with the axle assembly in the vehicle.
You are correct that you need to remove the rear cover so you can pull the axle shafts out of the carrier. I strongly recommend that you plan to replace the axle shaft seals when you do that.
The "trick' is that you need to slide the axle housing to the rear far enough so that the whole differential carrier assembly is out of and ahead of the axle housing. You will need to support the carrier assembly and torque tube as you move the axle housing to the rear. You do not want that assembly with the torque tube to drop beyond normal travel.
Take a look at the distance between the top of the leaf springs behind the axle and the bottom of the frame rail. That distance decreases as you look to the rear. If that measurement gets as small as the outside diameter of the axle housing tube, that becomes the rearward travel limit. I do not expect that will be a problem. Just check it first.
Remember that there some locating pins to hold the axle in position on the springs. You will need to lift the housing a little bit to clear them in order to slide the it to the rear. And watch the brake hose!! I expect it is not long enough to let you slide things to the rear as far as you need. Obviously you will also need to disconnect the parking brake cables.
