What I am getting from the conversation is that you transferred the wrong character by accident and Square Enix won't not refund your money because the proceedment requires you to check the character you're tranferring and confirm it. I've never heard of getting a randomized re-designed character when using the transfer service and I have used it a few times myself, but if what you're saying is true you might need to provide some sort of proof. The suppor team is only doing their job and there's so much they can do in this situation.