Ah! (I don't check my visitor messages often, sorry for the delay!)
Those grommets!
I had a Nighthawk that leaked a little around those, and I tried just about everything to keep it from leaking. (Even Crazy Glue!) In the end, I wound up pulling the valve cover and replacing them, using some Permatex HPV sealant on them. Never leaked again.
The downside to this is that on the Nighthawk, pulling the valve cover was a 30 minute job and on the Shadow, you have to remove the engine.
Actually, I don't quite believe that, as I'm writing it. You don't need to remove the valve cover, just lift it enough to remove the rubber plugs. You may be able to do that if you remove the fuel tank. That may give you the 3/4" of lift that you'll need to get new plugs in.
My bike is an '86, and the geometry between the engine, frame and everything else it a different than it is on the 83/84/85 versions.
Let me know what you find!
--Justin