I also noticed this the 2nd time I ran through the campaign. Going on my own sort of "maximum-fun" trek, I opted to go for extreme overkill with heavy fighters and torpedoes. After completing the campaign I noticed my battleship kill count at only 4. Quite disappointing not getting all those kills registered for a screenshot at the "Find a Job" after completion, I went looking around a few files and believe that these are, in fact, mission/campaign only solars that would go into a counter that kept track of targets destroyed such as Large Space Stations and the like. Anyway, back onto the main topic at hand I'll share my track record through the campaign.

Dagger equipped with Adv Scorpions and Pyros 1 Turret. Kept this until after the Hovis race and then went with a Crusader and full Pyros setup. This lasted me until I picked up a Dragon just before Tekagi's Arch which I loaded up with another full Pyros setup and a Borocco. Stayed on with the Dragon until the Osiris and I picked up the Anubis for the real fun to start. Here's the loadout I had for the last few story missions and even a while afterwards:
6 x Angelito MkII
1 x Debilitator Turret (until after battling Rheinland, where I switched to a Pyros Type 2, weapon speeds and targeting problems don't really bother me)
Rippers and Starkillers added a little flavor to the show, along with using Moonstalkers/Catapults to give me greater destructive capabilities

Overall I do believe the campaign was a LOT more enjoyable this time around, and having all those extra weapons on afterwards (no need to sell them. oh, the joys of looting the entire rim of Sirius ) was quite helpful in giving me a variety of paths to branch off on. Thanks to Sherlog and T-hawk for giving me great ideas on where and how I could come about some of these quite potent weapon combos, and what I have accomplished in MP servers with them.