Honestly, my method for dealing with AMM spam in the early game is to just not use offensive missiles.
I DO use AMMs myself, putting just enough research into missiles to have a little bit of a decent multiwarhead capacity and letting engine technology do all the heavy lifting. Since NPR AMMs tend to have 1-point (or less) warheads, it doesn't take all that much armor to just shrug them off. Even better if you have shields.
AMMs on my ships are for when the hostiles launch stuff that's obviously too big to be an AMM, and might actually be able to hurt me. I usually keep them caged unless that "this could hurt" threat shows up.
The research I "saved" not working on offensive missiles goes into better fire controls, longer direct fire weapon range, and better engines.
Later in the game, I run missiles big enough to have 1-3 decoys on board. I've also embraced carriers, as fighters give you an excuse to put a BUTTLOAD of box launchers into a fight and just swamp the enemy with literally hundreds of ASMs (preferably with at least one decoy each) launched all at once. Plus, they're fun! Maybe inefficient as heck, but definitely fun
