Now this sounds more like it, one little bubble will be the expansion as the motor warms up, exactly the reason the breather is there. The oil on the sprocket will be from a duff seal, crap from the dirty lanes it has spent its life traveling down with a big bloke + kit at no miles an hour.
Also the piston, running slow 'riding the torque' is actually not all that good for a 2 stroke either, they are actually beast suited to generators and such where they can be left running at the ideal rpm where the piston 'floats' in the centre of the bore. Extreems of rpm no matter high or low will cause excessive wear, it has probably spent its entire life on choke to boot which will add to the piston wear.
It sounds to me like you have it nailed, it certanly ticks all the boxes for me. Unfortunately there is no easy way of cleaning the pipes. All the options are either flammable/toxic/corrosive/cost in various combinations.
It may all be relatively soft and oily, parrafin (or lamp oil, thats cheaper but the same stuff) left for a day or 2 or diesel.
Or if you are carefull and use gloves ,goggles etc get yourself some caustic soda crystals, proper stuff not that cilit bang crap make it up good and strong and leave that in there for a day or so.
Or! Fill the tank pick a looooong road and thrash the living daylights out of it till the smoke stops .