Ooh!! This is your chance to make friends with the Dyson Golem -- or at least tick them off at the AI. If you can maintain a military presence on that planet, the Dyson Sphere will attack both you and the AI on it (assuming this is the planet with the Dyson Sphere, and not one adjacent). Since the AI outnumbers you, odds are the golem will kill more of them than of you, especially if you stay away from the golem. Then, if you're feeling brave, you can kill the command station on that planet and all of the dyson ships that are then produced will attack just the AI and not you. Just be sure not to build a command station of your own there, or the dyson will get REALLY pissed off at you and will definitely kill you on that planet.
Beyond that, the lightning warheads are a good idea for clearing big clumps of AI ships. You can even nuke them if you must, since it's only a IV planet. Only downside to that is the AIP increase. I have recently really been loving transports, honestly, because they no longer suicide all the guys inside them when they die. So you can use those to slingshot your forces across the IV planet to specific attack points, and then your guys burst out in a blaze of gunfire and take down their targets (or something like that, anyway). Might be helpful!