I'd pull the cylinder off and see what's going on. It's not uncommon for the ring to get stuck due to excessive carbon, causing a loss of compression. That can usually be cleaned up easily. If it's scored then you'll have to see how bad it is.
I doubt it's too much oil as I use 50:1. I had the muffler apart and the spark arrestor was removed and cleaned really good with brake cleaner and a wire brush to the point it was like new. Still going to play with the adjustments some more as I've replaced the carb, all gas lines except the on in the tank (looks fine, going to replace anyway just in case) added a chip to bypass the points and condenser, replaced the spark plug, cleaned the muffler/spark arrestor and started with the carb set to owners manual specs and slowly moved them from there. Not wanting to tear it down to the cylinder but I may have to. I really want to use this saw so I'm not putting too much strain on my ms250. The ms250 is perfect for everything 12"-15" and under but once they get 16" and up it takes longer to cut.
I'm betting the crank seals are shot, running lean is often an air leak which can be a crankshaft seal, I got a free Echo weedeater from work that way, the seal was just pushed out somehow, and needed a regulator diaphragm, pushed the seal in and replaced the diaphragm and have put many gallons of fuel through it...
Sounds like you covered most other options, unless one of the sealing surfaces on the jug are bad it sounds like crank seals to me, if not aviation seal or indian head sealant could be your friend...
Finally borrowed a compression tester. Got 100 psi after a couple pulls. So after reading some forums, these old 031av's should be well above 150 psi. Some were saying 175-195 psi. Mine gave up after 100 so I need to get rings for it for sure. I was trying to see the piston by removing the muffler. I took out the couple screws I saw but it wouldn't budge. Like there's a screw holding it from the back side. I didn't take any covers off besides the cover over the chain nuts. It was late and I wasn't in the mood to eff with it. There's some cheap pistons with rings on ebay but I may just need rings.
I've had the other side torn apart when I installed the chip to bypass the points and condenser. I swear I took the muffler off before to see about adding some extra holes but it must have been a different saw.
compression is hard to go by on a 2 stroke, but 100psi is getting toward the hard to start and lower power side... maybe try putting a few drops of oil on top of the piston before checking it again... sometimes it can be a carboned up ring as well, if it is sticking compressed it isn't going to make compression. On small 2 strokes the top ring is really the only one doing work, some people remove the second rings if they are even there (many are just single ring).