So, I cheat tested this mission a little bit, and I found that if only the Carthage was left, there would be no damage done to either the AO or Katana.
I know we were really distracted with a lot of different bugs, including the uberbombers, but looking through the mission myself, the likeliest cause of the Katana dying really fast is the fact that it's on Heavy Armor 100 the entire mission.
Is there a specific balance reason why this was done before? As things stand, balance is broken, and it would probably make the mission less grueling to add Heavy Armor 80 to the Katana right after it jumps in. Although I haven't tried it yet, and I'm about to.
Also, on an unrelated note. After closing and loading Freespace again, the Indus refused to take on its hull strength from the checkpoint data, strangely. May just be my computer acting up.