I recently made the mistake on getting in Precursor's AMM missile range after having no trouble against their ASMs.
When I got into range of the their AMMs a few of my AMM ships were already out of ammo and even with 9 quad-turreted gauss cannons I would get hit on every volley, there were 2 salvos of 45 missiles each and I don't remember how many salvos of 4 missiles but they added to almost 200 and my 40k kms tracking speed was no match for their 77k kms speeds.
It was a massacre, I thought I could pull through it, but I that's when I realized how little MSP I've given my gauss ships, failure's started appearing and I lost that whole fleet in the engagement.
I also learned then that putting 9 lasers on the same BFC is overkill.
One problem might be that your turrets was way overkill for the smaller salvos of AMM. Each turret can only engage ONE salvo at a time. It is often more efficient to use smaller gauss cannons so you don't overkill salvos as frequently. If you had 18 quad 50% sized quad turrets those salvos of 4 missiles would probably produce much less overkill.
I also think that nine total turrets in a fleet probably is a bit small, unless your fleet was small.
Armour is also a pretty good way to soak AMM as well if that is your intention... but that works best on really large ships who can afford many layers of armour.
You also can keep some of your own AMM in store and shoot them at the enemy ships rather than their AMM, that will force them to shoot at your AMM rather than your ships and you will eventually drain their AMM storage. You also can withhold firing ASM until you are really close of you carry ASM which also will keep their AMM busy shooting at them instead.