AIM-54 was a Navy only project, not an A-12 armament. Perhaps you're conflating it with the AIM-47? The Phoenix is a natural derivative of the Falcon, but still a distinct system.
Fun trivia: in 1980 there was a study about modifying existing SR-71s to carry AIM-54s, to shoot down Soviet AWACS planes. It never went anywhere, but it sounds pretty bad-ass.
Great link. I'm surprised that this was contemplated as I've always thought the Moss and Mainstay were considered crappy AWACs. It's also interesting that the Foxbat wasn't considered a threat to this mission. This also gives a lot of insight into the role of the F-22 should we fight a near-peer opponent.