For support to help recover the storm ID and games, they would need to have information from you to prove it was your game .
I am not sure of all the types of security questions and answers that they would accept, but if I was in that situation, I would take a stab at it and provide them information from my iTunes account. Like the day I first downloaded one of the games. The actual day and specific gem package I bought etc.
Things from my account that an support agent can match up and that I would not give out to anyone else.