FWIW, my feet are similar to yours in that I have a naturally very high arch but I'm a hugely sloppy overpronator. I'm trying to work on the body mechanics
but in the meantime I use orthotics in stability shoes.
The ones that work for me are AmFit orthotics, where a pin machine scans your foot in a non-weight bearing position. The ones I've had made either weight bearing or with the orthotist pushing my foot down into the mold, did exactly what you said: cast what was wrong with my foot.
So I hope you'll have good luck with yours.
Speed comes from what you put behind you. - Judi Ketteler