Yep, it's all three.
I just use a truck tire and run over it. But that works.
another use for the backhoe! i used mine to till our garden this spring..lol..i have used my woodsplitter in the past to break beads.
I just use the stabilizer and a block of wood but don't have a cab so can stand beside the machine to work the lever.
I put in 2-in poly pipe in the winter and I used it to straighten the pipe out. Wrestle one end of it under the front bucket and set it down wrestle it underneath the outrigger and put it down, then roll it out and put the back bucket on it and go drink some coffee and let the sun hit it.
As Dave said, use a stabilizer. You have more control of what you are doing. The backhoe can be hell on lawn mower rims.
Old school
I started by holding the wheel down with the stabilizer and pushing down with the bucket but the way I have it in the photo worked best for me. Not sure how damaged the tire is but it shows no signs of being torn.
NH575E, and you said that you shoulda rented...LOL! The possibilities are limited only to ones imagination, as to what these machines can do.
Done that a number of times when the bead is stubborn!!