Ben, Let me offer my 2 cents worth.. First. I worked for Homelite Chain saws for 10 years on the bench and running a service center. (Just wanted to give you my back ground). Now about your problem... As far as cleaning your carb is concerned.. you can't really do that unless you remove the Welch plugs which cover the small passages in side the carb body. Its possible.. but not likely .. that something there is floating around. I say not likely because if it were dirt were in suspension and then covered one of the small outlets.. your engine would go leaner. The Inlet Needle valve could be sticking once in a while. That is the needle which allows fuel to transfer from the pump side of the Carb to the discharge, regulated side of the carb. If this needle is sticking and not closing when it should it would cause a rich condition.
I don't know how good their ignition is but usually they either work or they don't. If its intermitent you can hear the engine missfiring . I have doubts about Syn oil being a problem inside the carb.. When I was doing Chain saw testing in our engineering lab we ran saws every day on normal oil and then we changed to Synthetic to cut down on the smoke in the lab. Did not effect any of the saws which represented over 35 different makes and models. My suggestion is if you cannot get your engine to run consistantly after all your tinkering.. send it back to Keith for a look.. I know this really doesn't answer your question but hopefully it'll give you a little more insight.. Regards BobH.