The ability to temporarily reset the "to best" marker to explore other paths is something I would like implemented. Perhaps this presents user interface challenges. Let me suggest one way it could be done.

Introduce "Ctrl-a" to "Ctrl-c" whith their "Shift-ctrl" counterpart.

They will work similarly to the current "Ctrl-1" to "Ctrl-3" except that it will place the puzzle in a state where "ctrl-a" will produce the best improvement to the configuration recorded by "shift-ctrl-a" (instead of that configuration itself).

To make it more visual, a letter "a" to "c" could appear somewhere in the screen.

The "To-best" button and key combination work as before. It produces the "real best" configuration.

Two GUI implementation possibilities when pressing the "to-best" button.

(1) It clear the "letter" state, reverting the puzzle to its normal state.

(2) Using the "to-best" button does not put the puzzle out of a "letter" state right away (it is useful to compare a "letter" configuration with the "real" best state). But any move performed on a "to-best" configuration clears the "letter" state.

I would prefer (2).