This all seems to assume the tank serial numbers would be captured at one moment in time ("captured 15 of these tanks uniformly at random.") But in fact the tan

This all seems to assume the tank serial numbers would be captured at one moment in time ("captured 15 of these tanks uniformly at random.") But in fact the tank shells dribble in over time which biases the gap, the gaps at the highest numbers are going to be greater. Earlier tanks have had many more chances to be destroyed or captured. So using average gap is clearly not going to give the best estimate. If you restrict yourself to tanks from the latest large battle, that will cancel out the dribble effect though.