My plan:
It took me some 2 fighter and 4 bomber wings to cripple a Sath, the fighters simply orbited near the hangar bay, and generally shot most of the SF's before they even had a chance to afterburn away and start a big dogfight, while the bombers needed 12-14 minutes IIRC to disable the ship. If the Sath has any escorts, I wouldn't bother to do anything with them, except for maybe disarming a beam or 2 to make the Hat's mission survivable.
If the Hat can stay in the battle area, it can slowly sink the Sath. If not, the SJ is already mission killed and we can move on to the next one.
In the mean time, the already stopped SJ will need to be watched, by stealth fighters, to make sure there are no repair ops going on.
If new tech is allowed, I'd add stealthy combat ships the size of Argo's, one loaded with AAA beams and Flak guns, the second one being a micro-carrier, and the third a stealthy supply unit. I'd also make a Pegasus variant that can load Kaysers and some more missiles, and another one that can carry Cyclopses (2 would be enough) and Maxim guns.
Such units would attack the Shivans behind their lines, hide easily in nebulas, dust clouds, asteroid fields, or even near single big rocks. The stealth strike craft would attack the Shivans where they are weak- cargo ships, transports and gas miners. That would keep the Shivans' repair rate slower than the GTVA could damage their ships, and after a few weeks their would be dozens of SJ's floating around, waiting to be finished off.
All ships would require quick charging subspace drives and massive sensors to keep one step ahead of anything cruiser size or larger (at least until the big ships wake up without beams and engines). They could also be sleepers during combat in their system (floating in some hiding spots), and activate once the main Shivan force moves beyond them, giving a safer environment to work in.