To counteract your idea that the warship is already moving directly away, making calculations invalid, remember that all missiles need time to accelerate to top speed, which adds on time.
During our calculations, we were both using ideal missiles -- sort of a term I'll be coining on-the-spot for a missile that can accelerate from 0% to 100% in an instant, can't be shot down by power armors running interception duty, and on top of that assuming the MEGAMI isn't actively maintaining point defense work.
Besides, we don't care about the missile and ship being made out of differing materials. It doesn't make sense to measure the speed of a missile, then put armor on it which slows down its top speed. No, we put armor on the ship and missile first, and then measure speed.
And again, 0.5c engagement range is a very short engagement range. A current production Mindy can cross that gap in a hop, skip, and teleport-fueled jump. In fact, most power armors can cross that gap in almost no time at all.
20s is a best case scenario. Most of the time, it should be a little higher.