Just to go off on a tangent slightly with regards the Korean Air 747- if you discovered whilst in the air that your fuel load was way off, is it possible in a 747 to select a certain combination of tanks and bring the aircraft closer to correct trim by burning/ dumping fuel?
Yep.
Too nose-heavy move fuel out of the centre wing tank and/or tanks 2/3.
Too tail heavy move fuel out of tanks 1/4.