When I was changing lots of tires for pivots, tractors, pickups, etc - I used a backhoe all the time. It was soooo much simpler than using the bars and spoons.

The method I liked to use was to bring one of the stabilizers all the way down to the ground, and then on the other side, bring the stab down part way, then wiggle the tire to be where the bead would be pushed off by the other stab, missing the rim. Hop in the cab, push down on the stab over the tire, poof, Bob's your uncle.