Anything listed as Flexible can be refunded to the original form of payment. I've found it's actually not too difficult to book these on aa.com. At the top of the results page, there's a slider that will only show Flexible (refundable) tickets. And once you select a fare, the first itinerary summary page (before you begin ticketing) may show the cost to upfare to refundable, and it's often $50-75/each way.

My biggest gripe with AA's Flexible fares is that once you've selected one, there is no indication on either the Booking confirmation, receipt, or My Trips page that the fare you booked is Flexible/refundable. The only way to know is to save or retrieve the fare rules, which can be challenging to read if you're not familiar with them. Then, if you cancel a Flexible reservation, the cancellation page advises you that your fare is safe as a trip credit to use on another reservation. The only way to refund to original form of payment is to fill out a refund request on prefunds.aa.com. If you know the system, it usually works fine, but I can see a lot of casual flyers either not realizing that their trip is refundable or getting tricked into thinking the refund is a trip credit (not realizing that trip credit is available for most non-BE cancellations).

This is in contrast to JetBlue, e.g., who clearly indicates in the reservation page if the fare was refundable, and if you cancel it, the credit goes straight back to your credit card, no additional forms required.