If it helps: my model G which is very similar in design to the J2 will also wetsump . I've paid attention to the crankcase halves & made sure the oil is not leaking from the oil compartment into the sump, it doesn't. The oil that's draining down into the sump is coming from the timing chest & getting past the bush.
Its not a problem if the bike is used regularly (i.e daily) but leave it for a while & the engine will smoke & chuck out the contents via the engine breather. Saying that its not "too" bad & clears pretty quickly (oh & leaves a mess on the floor sometimes) after a minute or so.
I did contemplate H's modified breather (as sold for the Bullets), indeed bought one & fitted it to the G; it solved the "puking" problem
however it just looked plain silly perched on the G's forward mounted oil filler! So I removed it. However, seeing & understanding how H's modified breather worked has given me an idea. What I intend to do is run the pipe that comes from the engine breather to the oil filler extension.
It might mean popping a few holes into the filler extension & mucking about a bit & experimenting but I don't see why it cant be done; hopefully the oil blown out the engine breather will go back into the tank. Any pressure from the engine breather that goes to the tank then vented out of the other side of the filler extension, in essence a
simpleton take on H's Bullet breather. If it works out ok i'll let people on here know.
I don't know if you do FB? On there there's a closed group called British Motorcycle Mechanics, anyway on there's a guy called Claude Besson (an RE enthusiast) with a cleverly modified G engine that doesn't smoke or belch
Saying that.... theres a bloke not a million miles away in Wales.... Bullet Whisperer they call him... & he built an Asbo G
(I'm not saying that the G s & Js are the same but they're in the same sort of engine family). I cant remember how Paul Henshaw tackled things when he did the G engine but i'm sure that if its like any of his other builds its pretty well good, give him a shout
best regards
Mark