Every 2-stroke engine I have ever worked on (this applies similarly to 4-strokes) has a sweet spot for idle adjustment: either side of it the engine runs rough, stinks too rich, stalls too lean or loses power. I's in every owner's manual I've ever read: adjust to highest idle, then add 1/8 to 1/4 turn towards richer, THEN set idle speed with the speed adjustment
In my case, it took about 3/4-1 full turn to bring the idle down with the idle mixture screw (as you suggested for the test), with an idle speed screw that's already non-functional (in its lowest setting). So, I don't regard this method to lower idle speed with the idle mixture screw an acceptable solution, especially with an idle speed adjustment screw that no longer works.
Back to my question: What do you think the test result revealed? What is my engine's problem?