I think you should have titled this Backhoe installation/removal! LOL
I sit my BH down on a heavy pallet with the stabilizers down and just before you disconnect the hoses ( I forgot to tell you this part)
lower the backhoe and subframe down all the way. It will be stabil then. Then shut off the tractor, release the pressure on the hoses and disconnect, move away from the tractor.
To reconnect, simply back straight up over the subframe to just before where it slides into the rear bracket. You'll need room to raise it up to the bracket. Now turn off the tractor, release the pressure by moving the loader joystick around until there's no loader movement, hook up the hoses, restart the tractor and adjust the stabilizers and bucket to level the subframe to the hooks and back up the tractor to put the subframe into the mounts. It takes a little practice, but it's not difficult. Put the pins in the subframe and raise the BH boom up, you're ready to go. The most difficult part is usually just getting the subframe at the right level for backing into the mounts.
John