Woah! Someone played my game... Thank you so much :)
That is a brilliant idea! Like, OMG that is amazing! Maybe having the player start in the past, and put up walls as you said, but then having them replay the "same" level in the future where things are broken down, and they can use that ability to bring it back. This also means they are more familiar with the layout of the level which should make for some interesting strategies. I can't believe I didn't think about what, you are a genius!