I'm sorry, but I can't take Coney seriously in this one. For one thing, it's not clear how much she's grown up since her mother's death - the flashback to when she took "Mom went to heaventhe Moon" literally isn't contrasted with anything. For another, she jumps too quickly from "Piloting the mecha is completely impossible for me" to "I must use our high-school sport mecha to fight the legendary monster that already took down two trained soldiers."
Couple that with how absurd the other team members can be, and they look too childish to be involved in this scenario - parody or not.