And to close the loop on this thread, I dined at this restaurant on Monday (my usual habit for this place). But unlike other months, where I've gotten only one credit per month in the AA program, I'll add one credit to the US Dividend Miles dining program as I've already received confirmation that the dine will qualify for those miles. Of course, I used a credit card not registered with my AA account.

I could just buy one large gift certificate each month, spend it over the course of my dines each month at this restaurant, and get all the miles in the AA program, but I'm just as happy spreading my earnings around.