If you took the quarter sized timing cover off the left side cover and put a timing light on one of the spark plugs, you should be able to see a timing mark at idle (or make one with a sharpie) and see if the timing moves when you bump the throttle.
I dont think an OBD2 reader would tell you much since its not fuel injected. I guess it might tell you the timing angle, Ive never tried that.
If the plugs are wet the carbs are rich, which does not make sense because you have to engage the choke a little to keep it running. Rich plugs means they are getting flooded, which could still be a carb issue, intake or exhaust flow issue, or the timing is so far off the mixture does not burn completely before the valves start to open.
You said early on the owner was riding the bike and then something happened, which would be a good thing, usually a single point failure is easy to isolate. Is there any chance the owner tried to fix the bike, messed with the carbs, left parts out, screwed something up, and (like many people) is too embarrassed to tell you what he did? It happens a lot, there are many motorcycles for sale that are "not running needs some TLC..." cheap because of this.
Last edited by KCW; 12-21-2018 at 08:54 AM.