Have you tried building a beam cruiser design to throw against these Alliance ships? I would expect the ships you described have an average armor in the mid-sixties, which is good enough for missile immunity but should get murdered by cruiser beams. I would be surprised if the average armor was high enough to shrug off beams. Even just one Cruiser Beam Laser or Proton Beam should be enough to break the armor, and after that it’ll be easy.
More general advice against tank fleets, particularly true (average armor >73) tanks:
To defeat tank fleets, you want to bring lots of rapid-fire weapons into play. Lots of high penetration weapons can also work, but as long as the average armor is greater than your weapon’s armor penetration a faster firing rate is probably more useful. This maximizes the number of lucky hits you’ll attain, which will slowly erode the armor rating of the target. If you also bring along a high penetration weapon (e.g. a Proton Beam), you can speed the process along once your lucky hits have degraded the armor enough to leave it vulnerable to the high-penetration weapon. Missiles are about the worst weapons you can choose for fighting anything with more armor than they can penetrate since they have such long firing intervals.
The best weapons for this purpose are the Fighter Pulse Laser and Fighter Laser Cannon, as the craft carrying these weapons will give you more guns per credit than any other ship design available, and the weapons themselves are among the fastest-firing in the game. If looking exclusively at armor-stripping, Fighter Pulse Lasers are slightly superior to Fighter Laser Cannons, but are more vulnerable to defensive fire and more expensive. Fighter Laser Cannons are the more versatile choice, as they perform much better in the dogfighting role and are only slightly inferior to the Fighter Pulse Laser in the armor removal role. You might also consider a dual-laser or a laser/pulse laser fighter if you can design one.
As far as orders go, I would suggest Cooperative/Vulture for strafing fighters, because that should cause them to pile up on one enemy ship at a time. This can cause issues if you have a mixed group of strafing fighters and dogfighting fighters, as your strafing group may try to cooperate with the dogfighters.