You know, I was thinking about this more, and just throwing it out there, but if you wanted to make it a different kind of challenge game, you could have the furniture automatically pop onto an open space every X amount of seconds and you would have to re-arrange the furniture to get rid of it before the house gets full (which is would be game over) and then as the time/stage progresses the furniture popping in speeds up making it tougher. Basically just full on Tetris, but done on a horizontal flat plane where you speed to re-arrange instead of arranging the falling block.
Now your game is totally zen and is a very opposite vibe of that stressful tetris kind of experience, but just throwing it out as an idea if you ever wanted to try to do a challenge mode.