I think Shrikes is better than Grimlers for this because it has longer range, though note you still need 2 shots to knock out the beam on a single mjolnir. Some of the miners escaped though, but this matters less.
What I did:
As soon as the mission start, order wingmen to protect the Serenity, slave the Narayanas and have them fire at the Radhanite.
Once the Serenity is in a save distance and there are no bombers nearby (don't have to wait for it to warp out), order your wingmen to hit an aurora each. At the same time, try knocking out one of the Mjolnirs with your Shrikes or Grimlers, use ammo pack and repeat with the other Mjolnir. Just when you fire your first salvo, order a resupply. If the frigates are done finishing off the Radhanite, have them fire on the miners.
Next, knock out the dishes on the AWACS. Be careful if you are using Grimlers instead of Shrikes since you will be in range of the point defenses. Again, order a resupply as soon as it is available. You want to resupply your missiles before you do the next thing. If your wingmen are done with the auroras, either have them hit the surviving miners, or either disarm the Carthage or just knock out the weapon subsystem to make the point defenses useless. Have the frigates fire on the minelayers.
Now it is time to scan the station. Just scan the necessary subsystems. Do the same with the two corvettes if you can. Depends on how much time you have remaining, if the frigates are done with the minelayers, then have them attack the corvettes.
If you are done with the corvettes it is time to call in the reinforcements, or if you are short of time however, you can just try and knock out the weapon subsystem on the corvettes and call in reinforcements. I only called 5 wings (gunships, bombers, stealth fighters, and a few other things) and order all of them to disable the Carthage. Once the Carthage is dead in the water, order all fighters to protect one of the frigates before you lose too many of them. You may have an option to call the Toutatis, but it doesn't matter. Have the frigates pound away at the Carthage and you can just sit back and watch.