I love the idea of having a "first run" leaderboard for the good improvisers and an overall daily best score. There could also be a overall randomly seeded best score, but you could see which seed the player used to achieve it, and play the same seed if you think you can beat it.
ps.: I do think though there is a big oportunity for cheating in the improvised game (eg.: you could play as a different user take notes of everything).