Surprise, Success!
My exhaustive testing indicated that the shortest path to the goal position in Scarne’s challenge was at least 71 moves long. I relaxed the criteria a bit, and obtained a solution which requires 72 moves, which (if I haven’t made an off by one error, still checking that out) is an actual minimal cost solution!
This solution doesn’t actually include the 5 hopping moves at the beginning (it complicates the calculation of the heurstic values and slows down the search), but I suspect I’ll get that figured out someday soon. Enjoy!