Instead of static buttons, use "Juice." Buttons should scale up slightly when hovered and "squash" when clicked.
A small corner element showing who you just passed in score creates instant competition.
Every GUI interaction needs a "click," "whoosh," or "ding" that matches the visual weight of the button.
Epic mini-games are usually fast. The "Play Again" button should be the largest and most accessible element on the game-over screen.