I've discovered the joy of fighter-bombers. One carrier, 20 bombers, each with 4 long range (at least 50m km) ASM box launchers. Don't even need to send the bombers anywhere- just have them pile out, all launch simultaneously, and pile back on into the mothership. With a CO that has a high fighter ops rating on your carrier, the bombers will be reloaded and ready for another salvo by the time the first one hits.
(Keep some escourts with AMM launchers near the carrier, just in case- not only can they shoot down enemy missiles, but they work well against fighters and beam FAC, too.)
Build multiple carrier groups. Your first strike gets even bigger. Any enemy fleet with enough AMM to shoot down 60 salvos at once is probably an enemy fleet you should avoid.