I think the most visually obvious oil is o the fin.. Must surely have flowed forward along the cylinder cooling fin surface, from the interface of reed and cylinder.. Where you removed a spacer.
Someone mentioned that the fuel/air mix has velocity and the reed snaps shut.
It certainly can't be the head if it's unburnt fuel/oil.
Just thoughts.
If you clean it and run it, can you not see the fresh oil appear again?