I think the biggest flaw of this game is that the player is allowed as many rotations as they want before they're required to make a move. This game sets itself up to be a test of precise reaction time, but once I realize there's no consequence for going at my own pace, it fails to be challenging for me. If ending the game due to a missed rotation seems too hard for what you're trying to make, a better solution might be to make it so players can take as many rotations as they want, but they won't be granted points unless it's the first. That way it's forgiving, but still gives you incentive to act fast. Why not have both, in the form of different difficulty modes?
EDIT: The changes made definitely make it feel more engaging now (also congratz on getting frontpage)