I have two personal AA cards and a business card that I got over two years ago. Normally my process with these types of card is to cancel when the annual fee rolls around, or if possible transfer to a card with no annual fee. In the case of these three, though, they have consistently offered to credit my account in the amount of the fee, which I accept as a general rule to keep as much available credit as possible. My understanding is that it's possible to churn the AA credit cards and get the initial bonus again. Is my best route to cancel the cards outright and just take the credit hit so that I can apply and get the bonus again?

I appreciate your help and apologize if this is an overly obvious question. Thanks!