This squarely falls in the category of, don't try this at home.
The redneck tire mounting solution is to have someone spray a flammable aerosol between the tire and its rim, and then light it so the air quickly expands, resetting the bead and inflating the tire.
Sometimes it works, like this:
http://www.youtube.com/watch?v=_M0GNLvPmAg
And sometimes it goes terribly wrong, like this:
The guy on the video said he had "nothing to lose" by trying this trick. What about his eyebrows?
BTW --- did you notice a little kid is nearby? This could have been much worse.