In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle.
In this context it reveals the usefulness of commutators, which are moves of the form ABA'B', where A and B are some sequence of moves and ' denotes inverse.
In general A and B aren't commutative, but with respect to a subset of the pieces, the actions of A and B are effectively commutative, so ABA'B' will do nothing to those pieces. Which means you can get some simple permutation control over the remaining (usually much smaller) pieces of the puzzle.
I believe this puzzle is equivalent to a Ehovxf phor ba n gbehf (rot13).
Both the "easy/medium" and "hard" puzzles look tricky to make in their own way, my gut feeling is that he "hard" puzzle is the easier one to design.