Pete, carburetor cleaner contains some pretty aggressive chemicals and was not a good thing to put into your cylinder. (Personally I wouldn't put it into a carburetor either.) It is possible for materials to get from the exhaust port back into the crankcase through the transfer port, but your Lawnboy engine has a reed intake valve, not a piston-controlled port. The reed valve is normally-closed (that is, it springs closed unless it is sucked open by incoming air/fuel mixture), so it should not pass anything back into the carburetor. It would take a lot of carburetor cleaner anyway, to slosh around in the crankcase enough to find its way to the reed valve. Long before that, it would have eaten your lower crankshaft-to-crankcase seal and made your engine run poorly, if at all. Did you ever check your crankshaft seals? This is normally done by putting each end of the crankshaft in turn in a vertical position, and trickling a bit of fuel onto the seal, while watching to see if it vanishes into the crankcase. Meanwhile having run the engine a bit since the horrible stuff went in there, chances are it has all been washed away by air/fuel mixture.
So far as crud in the carburetor is concerned, carburetor cleaner contains powerful solvents that should remove all the gum, oxidised oil, and any other sticky stuff. However it does not dissolve dirt or metal particles, which can sometimes lurk in the corners of drilled passages. The solids are normally removed in a second operation after using the cleaning agent: every passage is blown out with compressed air. This requires completely dismantling all kinds of tiny bits first, because otherwise the compressed air can destroy them.
I suggest you confirm that there is a lean mixture problem, by slightly choking the air intake. That will make the mixture as rich as you like. If the speed keeps cycling even when it is obviously running rich, you have a sticky governor, not lean mixture.
