Isn't most of this "dirt" really smoke? I remember that the L10s really smoked up on startup. And, when the winds were right, the smoke would blow right past the cabin windows and I would guess to the top of the plane. If it were smoke, not just dirt, this would explain why the dirt would not wash off after the plane was in a rainstorm. Also, we notice that the older planes, with engines that smoke more, tend to be dirtier. Coincidence? Maybe just age collects more dirt, but I think it has something to do with smoke also. Plus, how would dirt get to the top of a plane?
As for how they clean planes, try to find that picture with the hangar filled with soap suds.