Great explaination Tom-
I have a much harder time getting the beads broke without damage than mounting them. I have a selection of pry bars (different widths,thicknesses and angles)that I rounded the tips on to be able to get the smaller bites as the tire is almost on. Trying not to tear the bead is the tricky part while trying to keep the balance of the tire in the small zone of the rim. The soapy water is so important for all phases of the tire mounting/dismounting as Tom said.
Good luck- as I've had to walk away many times and try again before achieving success. I keep a container close by with my spare colorful language stored, just incase walking away doesn't feel satisfying!!