Special Stage is often best used later in the game, given that it takes more stars and protects for more turns. As a result, President's Privilege is advised as it can substantially reduce the price of using the hyper and make it easier to gain a star profit.
Play of the Gods is a particularly good event for the Cuties as the card itself counts toward their passive ability as does the card it activates, giving the player 2 stacks of Events Crashed (assuming the random event card called hasn't already been played the cuties).
Arguably, one of the best event cards for the Cuties is Party Time. If well-timed or accidentally triggered by an opponent using Play of the Gods it can cause every opponent to be in range of Special Stage.
As the Cuties are a highly card-focused unit, Home Improvement serves as both a cheap level 1 event card and a means to grant more opportunities for card draw.
The player should mainly be concerned about the Cuties' hyper more than anything else. The player should either try to stay away from tight sections of panels and the Cuties themselves in the late game or quickly KO them to avoid their hyper's activation.
Certain characters with event hypers that do damage such as Magical Inferno, Gamble!, and Air Strike can be used to KO the cuties while their hyper is active. Special Stage only protects them from targeted boost cards.