Here's how I ended up beating it:
Step zero: Arm your fighter with quad Sidhes, an ammo pack, and Shrikes. Make sure your wingmen have Sidhes, UX Accelerators, and any good dog-fighting missile.
Step 1: Order your wingmen to protect the Serenity. Although it's under heavy beam fire at the start of the mission, it does get clear of the beams with plenty of time. It's the bombers and heavy assault fighters closing in on the serenity that are the problem, full of evil cyclopses and maxims.
Step 2: Switch artillery from free fire to slaved mode and designate targets. Start with the closest Tev corvette, and also go ahead and mark the four gas miners too.
Step 3: Target said Tev corvette and kill the beam on the side facing the serenity with a Shrike. Without that bit of extra damage pouring into the Serenity, you will almost assuredly save the ship. Probably with a lot of hull left over.
Step 4: Fly forward, to the Serenity, following your wingmen. Lock onto the Carthage, and take out the beam that it's using to bombard the fleet, again with a Shrike.
Step 5: Call in for a rearm. Take careful note of the warp-in point for your repair ship; it's about 45 degrees to the right and 30 degrees up, facing the orion, from the Serenity's location.
Step 6: Reload with your ammo pack. Switch to dual-fire mode. Lock a Mjolnir's beam cannon and give it a pair of Shrikes.
Step 7: Your wingmen should be tearing the Serenity's pursuers to shreds by now. Use the Sidhe to blow up any bombs they missed while your support ship reloads your Shrikes. If you feel the need after reloading, you can go blow up some unwitting Tev pilots.
Step 8: You should be just behind the Serenity now. Stay there. This is an excellent position from which to claim a HUGE advantage in the coming firefight. Your support ship is right next to you, with unlimited Shrikes for you. Blast the second Mjolnir, which reduces the number of beam cannons pointed at your fleet to zero.
Step 9: Target each of the two corvettes near the Carthage. Give their lateral beam cannons one Shrike apiece. They're not pointed at your fleet yet - but they will be soon. Deny the GTVA every beam you can. When the Serenity jumps to safety, order your wingmen to cover you.
Step 10: Next blow up all of the Carthage's radar dishes with Shrikes. They take two apiece. Yes, just keep rearming.
Step 11: Order your artillery frigates to bombard the two minelayers into oblivion.
Step 12: Begin your 'attack run'. Make sure you have at least two Shrikes aboard for this. Fly up at approximately a 45 degree angle, over the Carthage and over the AWACS. Once you are above the two AWACS ships, target their radomes and give them one Shrike apiece.
Step 13: Ready yourself for a dogfight and scan the station's communication, weapons, and sensor subsystems. There will be Aurora, Kulas, Nyx, and Atalanta defenders. Your wingmen are good at slaughtering them, but if something gets close enough to you to take out with your Sidhe, take the shot.
Step 14: Order your artillery frigates to bombard the two corvettes near the Carthage. Fly up and over, back to your frigates, exactly the way you came.
Step 15: Once the corvettes are blown up, you should have nearly every objective on your list complete, with plenty of time to spare. Now it's time to sit back, relax, and call the attack. Even if you didn't blow up all the Auroras, you should have points to spare. Order your frigates to bombard the Carthage.
Step 16: Wing by wing, give them orders. Tell the bombers and gunships to disable the Carthage. Tell everyone else to 'engage the enemy'. Although you did scan the subsystems on the station and upload the virus to all the sentry guns, and they're mostly busy shooting down missiles, the 'engage enemy' order should sweep everything off of the battlefield that can possibly hurt your reinforcements. You can even order Falcata to help them if you want.
Step 17: Once the Carthage is disabled, re-order the bomber wings to destroy the Carthage, and re-order the gunships to disarm the Carthage. Sit back and wait for Lopez to beg for surrender. Accept if you feel forgiving & think a spare Ubuntu Orion would be useful later in the story. Vaporize her if you feel vengeful.
...Did someone say that the Toutatis got BLOWN UP in this mission?! I did not think the Toutatis made an appearance in Her Finest Hour.