You are correct about the rules for assigning damage, Gary. However, the ship surrenders when the last box is covered by a damage counter, not necessarily filled up to the burden value (page 18 in the rulebook).

I think that the value needed in damage counters to fill a box is set at the burden value for all boxes to keep the system simple. However, you could apply a different system as a 'House Rule', see whether it improves the game and make a report.