I would have thought that a small amount of damage on a flap wouldn't cause much of a problem as long as it would sit flat without big bits missing. As for the heavy tire, that is very odd. It's not a run-flat but all that extra rubber got there somehow.
I have had success in the past using the stabilizer leg of a truck with a crane on it to crack the bead loose. In your photo of the pickup and tractor you do look to be achieving something. I know it is hard work cutting tires off - I burnt out a nearly new 9" angle grinder doing it once.
David
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