Work out which widgets have to move. Then move only those.
250 boards, easiest first. Every one is verified solvable in exactly the number of moves shown as "best".
Fill every square on the shelf. Nothing may be left hanging below it.
Best is the fewest moves the board can possibly be solved in. It's calculated, not estimated — so it's always reachable.
Tap copy, then paste it to me. It's just numbers — no personal info, nothing leaves your phone unless you paste it.