Assuming you have the rear wheels lifted and the frame on jack stands, the torque tube will pivot up as high as the floor board and as low as the ground, quite a bit of movement indeed....
Glad to see you're going to place a jack under the tube, good. Theres some downward torque on it once you disconnect the U joint (or as Chevy called it, the trunion).
Be careful bending back the locking tabs on the 4ea U joint bolts as you'll be reusing them on reassembly.

Follow the manual on setting the freeplay on the ball collar. You probably know this but mentioning it all the same.

I removed the rear tranny cross member (5 bolts per side) but I was doing an engine/tranny swap and had to rebuild the rearmount as it has lost all it's cushioning material. I slid the cross member back to support the torque tube during this process.
That said, I believe theres enough clearance to do your repair without removing the cross member but you'll need to remove the 4ea bolts that secures the rear tranny mount to the crossmember and slightly lift the rear of the tranny to get enough clearance to move it out of the way of the ball collar.

Good luck
Dave