Show HN: Turnabout - an iOS puzzler I'm still trying to wrap my head around

OP Here - A programmer friend and I made and released this recently, thought some of you might find it interesting. I did all of the artwork and design for it, he handled the initial concept and programming.

Question is - I helped make the damned game and I can't seem to figure out the underlying strategy. Can any of you? There has got to be a way to solve it to get high scores, but no luck on my end and my buddy isn't giving away any secrets.

Thoughts?