Can I pay a store credit line with an Amex card, at NO extra cost?

Unless you use a balance transfer offer, you generally can't pay one credit card with another one. The reason is that the credit card company you owe won't accept another credit card as a form of payment. And while the Starwood card does offer a balance transfer feature, it's not at 0% AND you won't qualify for Starpoints based on a balance transfer. So as you said, I think you are out of luck on this one. However, the Starwood card is an excellent travel card. Best of luck!