Nobody attempted to find the optimum solution where "round-the-corner" and other two-step moves of a single piece are counted as one move. It's not the same thing as optimizing for one-step moves and then merging adjacent moves of the same piece. The 112 step solutions merge down to about 96 steps, but it can be done in 79. I have placed the solution on tall_man's scratchpad.

The code I used to solve it is OCaml, but it could easily be converted to perl.