Here are a few moves for solving Rubik's Slide (in hard mode). If you number the squares from 1 to 9, each sequence swaps square #9 with another square.
8: D + R + U + L + D + R + U -
7: U + U L + R + L + D + U + U -
4: R - R + L + D + U + U + R + U
1: U L + R + L + D + U + U + R -
I'm working on a more efficient solution, but using these sequences, you can solve the center square first, and then use these moves to swap any two squares on the outer ring. For example, to swap 3 and 9, you can do a "++", followed by the sequence to swap 7 and 9, followed by a "--".
