It isn't solvable, I am willing to put money on it. Not proven rigorously, but mentally one can set up the balls in the final positions and run the puzzle in reverse. the rules change as they can only move orthogonal to a wall or ball they can "push" off, then you can see they can't end up in any configuration which is reachable in the start state, running the normal rules. Keen to hear if if I am wrong OP, but with me andy friend both having 30 and 15 plus minutes respectively, I would imagine we have gone through every possible configuration by now