Dave . . . not sure if this idea would work for you or not; but with tyres/rims that need that sort of manipulation I've found a shovel to be very good at making things easier.
Slide the blade curved-side-up underneath the tyre, put one foot on the handle, and swing/swivel the tyre on the blade, lifting or dropping your foot at the same time as appropriate.
Might not look very dignified; but it works in most cases!

Just a thought.