My usual trick to make USD bookings on AA.com with my Canadian credit card is to use PayPal as my payment method on the US site.
But last time I made a booking, I was redeeming a travel credit and PayPal wasn't a payment option, so I just put my billing address with California as the state and the old gas pump trick for zip code and it went through (A1B 2C3 = 12300). This was with a Brim MasterCard.