Usually the strap idea woks pretty good, I generally stop at as little pressure as possible, once the bead touches and the air quits hissing out I stop and release the strap, there will still be massive force on it. I have never had as much trouble as you did, but without the strap I don't think I'd ever get one on. I have never had to try this on skidsteer tires, but sometimes on car tires I have lay the tire on its side, reached through and pounded the one bead partially on until it sticks, then suspended the tire on a couple blocks and pressed the rim down while inflating.
I have used either in the past on truck tires, It works best if you put the can in 120 degree or so water to warm it up, takes a lot less either to get the results, makes its puff rather then just flame, Have a propane torch or such to touch it off, the longer the handle the better. Now I buy Michelins, they just pump right up.
Obviously you do this at your own risk, as some people have been serious hurt. Spending money is always safer then getting dirty, but some has to get the job done.
Ken