Pretty neat puzzle. Maybe a little bit too complex at moment, filling levels with a lot of overwhelming content (paths and moves) that just make them laborious to read. I'm more a fan of concise puzzles. The last level is well done in that regards: every bit of level has a purpose, so solving it is really about reading the level and planning moves.
It's still a nice concept. Maybe it would benefits from a little more visual effects ("forced moves", without reading the description, feels a little weirs). But it's an interesting twist on sokoban that fits well with the theme! Like I said, analyzing the levels and anticipating movements was interesting. :) Good job!