My solution to this problem was to go with fast size 1 missiles, staged for long range. In fact, I think my standard AMM and ASM use the same engine. (Actually, I have three or four ASMs, but the one that gets used as the final stage has the same engine as the AMM.) I also have a decoy which is just a tiny bit faster, and has armor instead of warhead. The advantage is that because of the way that the FC allocates defenses, it's going to soak up the first salvo of AMMs, and all the PD until the decoys are dead. Seed one pod of decoys in with each salvo of real missiles to double the number of individual targets, which slows down the AMM firing rate. And remember that adding FCs makes getting through PD easier if you can generate more individual targets than your opponent has FCs.
Also, laser heads have started working? I may have to fire up a game and test them. Last time I tried, they were completely useless compared to normal warheads.