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You can product change the card but considering how new the account is you have to wait a year before you can. So in some way the rep was right.
It is what it is even the higher line reps don't know everything and (this is not directed at you but in general) if the question/concern is not asked right that can confuse reps as well. Plus enviroment of a call center is not for everyone. Doesn't excuse it but it happens.
It sounds like you want to do a 0% balance transfer. I see you listing Citi Diamond Preferred in your signature block. That card often has very good balance transfer offers. Why not use it for the balance transfer and use the Chase Sapphire Preferred as your restaurant card?