My Atlas/Dommie oil tank began leaking at the filler cap as you describe.
I removed the 50 plus year old neoprene (rubber) gasket in my oil cap and made a replacement using several different materials. What worked best for me was 1/16 inch thick synthetic cork, available at any auto parts supplier. There are 1/8 and 3/16 inch thicknesses available, but I would think you can just double up the 1/16.
Since you are already using cork, check that there is no crud on the floating plate inside the oil cap, and check that the filler neck top is flat.
I believe synthetic cork is superior to the natural type. I also believe if you cannot get a good seal with synthetic cork, something else is wrong. Check the crankcase breather vent as Concours has suggested.
Slick