This is an awesome level. Was stuck wondering what to do for a while. Found a 4 cut on my initial solution, then another 4, and then had to do things pretty differently to take off 2 more, before I got the final 2. Really brilliant, you make excellent levels.
Really cool concept and execution. I have no idea why that path saves 2 moves - I'll have to go back and inspect the level a bit. I like this one a lot though. Hard to even see what to do for a while at first.