I think you could keep the timed aspect, but the current format of the game makes it too prominent for those of us who are primarily interested in reducing the guesses. The first thing I'd do is get rid of the sad faces for missed stars at the end. As silly as it sounds, it feels like being penalized for approaching the game more methodically.

If you just show the number of stars the player got at the end without emphasizing what they missed, those who are playing for speed are rewarded with more stars, those who are playing for low guesses are rewarded for a low number.