I would vote for buying a brand new carb if you don't have another one to test off a good running 346, I always like to have an extra good carb to make diagnosis easy on all my model saws, plus these 346xp carbs are like $30 shipped to your door, make sure the get the real oem zama and the proper one since they are different for the OE and NE due to primer bulb or not. Plug looks obviously rich, so when you cut on its side any of the fuel mix pooling at the bottom could make it even more rich. Also agree turning the H and L screws is easier with cover off (but more dangerous) since the screwdriver angle is not straight in, that said if you took the carb off, you should be able to confirm it was completely turned in. Also, when idleing the saw should die when the L is turned all in.
With carb off, a vacuum check would be good too, there is a universal flange that works. I also changed the clamp to a large stihl style screw clamp, and you could also use an extra plastic flange that the long carb screws go into since they are easy to overtighten.
good luck.