I guess that the crankcase lever is actually operating from a flap in the cooling shroud and responds to airflow from the fan blades on the flywheel, shutting down the throttle when the revs pick up.
I have a mower that works that way, and which has the non adjustable carb too, although it's a four stroke.
It had exactly the same hunting problem, and being unable to find anything that would act as a damper on the throttle so it would be slower in responding to changes, I eventually took the whole kit and caboodle off and fitted a lever throttle and cable so I can control the engine speed manually.
When I can be bothered, I shall add a needle valve adjuster to the main jet.
I should try cleaning the air filter before you get radical with it though- hunting is a classic symptom of rich mixture especially in two strokes.
Cheers
Dave
(Two-stroke guru as well as musician)