Transplanting Trees with a Backhoe

I've done that some. The picture is Old Stoney and me, moving a clump of pampas grass. Success with trees and shrubs depends mostly on variety, I think. The more robust types (I've had near 100% success with hollies, crepe myrtles and ligustrum) will do well where more tender sorts (think dogwoods) will wither when you walk up to them with a shovel. As for technique, I'd recommend always dig the destination hole first. If you get where you're going and have to dump the transplantee and then pick it back up after digging a hole you've tripled the trauma. Prepare the hole as you would for any new planting - good size, good dirt, compost, mulch. Be prepared to water daily for the first week or two, regularly after. Never let it get too dry. When you go after the plant use the hoe to cut into the ground around it at the edge of where you think the root line will be, well out past the edge of the branches. Then when you scoop try to go for as much root and dirt as you can get in one scoop. I find that it helps when carrying the plant and root ball from place to place to have a load in the front end bucket. Makes steering more comfortable. Hope this helps.
Good luck, Wm

A google search on transplanting trees will give you several ideas and recomendations for root ball size.