Played around with Invictus more, sicced it against a 300+k Hegemony bounty, and things went easier for me than without it. Invictus just chews through cruisers and battleships with its four main guns. I brought Pegasus as a backup, with the rest of my fleet with spare random clunkers for Hull Restoration to fix while I travel. Invictus took some damage, but was in no danger of dying. I only swapped to Pegasus once mainly because it got isolated from the fleet and wanted to move it back closer to the fleet before it got picked off.
Next time, I probably will replace one of the Xyphos with a Sarissa. I found more Gauss cannons, but I discovered none of the turrets fire while the Lidar is on, and I rely primarily on Lidar boosted guns.
So far, my use of Invictus is generally turn on Lidar, fire the hardpoint guns, vent, repeat.