You don't need to start over to beat it as the other characters. Just go to continue and then the final boss, after that choose the character you need to beat it as.
I love the game, and it an amazing concept. I am just glad houses aren't built like this irl.
Another thing I am glad about the game is, you can't accidentally destroy pieces.
I gave it 5 stars and favorited before I even started playing. Not just because the first one was awesome, but because I love penguins, the only thing that can make this game better is to add corgis :P.