I’m willing to bet that they somehow locked themselves into using 8 inch disks in the early to mid 80s if not earlier, when the 5¼ discs were still new-ish and the 3½ were brand-new or not even available yet.
You nailed it. The contract was awarded in June of 1988 and the ship was being designed in 87/88. That means the targeting system was almost certainly designed in 85/86. A time when 8" floppies were still prevalent in Industrial, Commercial, and Military systems.