Riddle Me This...oil Out Of Exhaust

The short of it is I'm looking for opinions on whether it is worth repairing this engine or not and diagnosing what the root cause is.

[Side Story]

Finally got to working on the engine swap on the VF500C. I picked up what was supposed to be a running engine for a fairly cheap price. Well, after I got the engine out of the frame, I went to take a look at the replacement which was in the back of the shed. The replacement engine is most definitely not a running engine. Hand grenade comes to mind after opening it up.

So this being the last PITA project to do before I can start on the stuff I actually care about, I figure I'd ask about what was wrong with the original engine (which turned out to be more than a dirty carb per the PO's statement).

[Story over]

First off was a broken tappet. So the valve may or may not have gotten hit hard enough to break it. I haven't got to trying to push the valve down or to buying a new tappet and nut. Otherwise the engine does turn freely and actually runs, sort of. Oh, and 0 compression on that cylinder. All other valves have been put in spec.

Big one is that I get a grey goo coming out of one side of the exhaust. It is the opposite side exhaust of the broken tappet. Not sure if it matters with the collector, but it only comes out on that side. The oil came out perfectly clean, and the coolant also came out clean.

I'm struggling to figure out exactly what is wrong with the engine. If it's rings, I'm going to get rid of the bike and be done with it. Actually, most roads lead to that result. If it was head gaskets, I would expect my oil to be dirty, or my coolant. But oil is getting pushed through the exhaust valves. I couldn't really tell too much which cylinder it was coming from, but I'll take another gander tomorrow when in different spirits. Any thoughts at all? I have a title for the bike, and it's actually in decent shape otherwise.

bump?

Can you do a leak-down test on the cylinder with 0 compression? It should tell you where all the compression is going, maybe the valve that's broken a tappet is damaged.

Head gaskets can be tricky, as the oil and water will only mix if the head gasket has gone between an oil and water way. If the head gasket's gone between a high pressure oil way and the cyinder, you wouldn't see them mixing.

BTW, the rear exhausts cross over in the collector. Which cylinder has 0 compression?

Other way around. The tappet is broken, but not sure about the valve. Left front cylinder, so I think it's #2. Which also has 0 compression.

I think I can do a leak down check. Trying to minimize the time wasted on this engine. I'm barely going to get my money back now if things work favorably (they never do), which is a driving force to just dump the bike and save my time.