Runs at FAST idle, not slow

Maybe try a bottle of propane. You could flow it in the carb throat and see if it will run on that at a slow idle. Squirts of starter fluid would work too. If not, you may have an intake leak somewhere, which you could also find with the propane (it will smooth out). If it does idle low and smooth with propane at the carb, that at least tells you it is the carb and not an ignition problem or bad cam.

Also, I just noticed you have been trying to screw the idle mixture screw in as much as possible. Don't go too tight or you can ruin the seat in the carb. Don't follow you on that. It usually dies because of too little fuel. Did you try going richer (unscrew)? Should be ~2 full turns out. It will also die if too rich, but usually dies smoothly instead of shaking, and the exhaust gets black first.