The 'murder by compass' AFE pest removal strategy:
1) Place a fortress with a snare, fire rate suppressor and mines. Cover it in PD - it might as well do something useful with the guns.
2) Create a death flower using kinetic artillery with shield regen boosters and minefields.
3) For best effect, try plasma/gauss cannon cruisers with a large plasma corvette screen. Shield capacitors are a must have.
4) Take your doomstack and split it into 4 component fleets. Place one on each of the four points of our hypothetical compass. If you have the spare influence/leader slots, try to grab an admiral for each with buffs to fire rate and hull strength. Gale speed is useful for the evasion boost as well.
5) Ensure the fleets are close enough to be within plasma range from the start, but not close enough to end up inside the enemy fleet.
6) Send a few raiding units into the AFE's territory to get their attention and lure them back to the trap.
7) When their fleet drops in, they'll be surrounded and all facing in one direction. The majority of (A)FE's firepower comes from their forward cannons. As at least 3/4 of your fleet will be out of arc, you'll minimise your damage. Given that your fleets are also starting in knife fight range, it's very difficult for XL guns to target.
8) As the fortress in the centre is such a puny target, it'll be targeted last after all the other fleets so it's free to provide that massive 25% fire rate / DPS debuff to the enemy throughout. Depending on the FE type, you'll also want to vary the amount of PD you take. Against Spiritualists, go PD heavy for ludicrous gib, for example.
If the above goes well, you've hopefully just annihilated an AFE doomstack with minimal losses. Replenish as needed and rince and repeat.