Definitely sounds fuel-related...
I have had one set of flatslides completely apart when I had a slide crack, and as I recall I was able to remove all the jets and do all the cleaning from the bottom - that is, remove the carb and flip it over to access the jets and passages. I also pulled the "idle/fuel" screws from the body and spray cleaned in that orifice, too.
Of course if you pull the body completely apart you can check for other issues.
The other "tuning" factor is to change the pilot air jets that are on the airbox side of the carb, they screw in the bottom area of the throat My 2000 motor's carbs has these, my 2005 goes not, and the 2000 definitely runs better off-idle.
3.5 turns for the idle screws seems really excessive to me! When I fiddled around with the 2005 600 and tried that, it idled poorly and had a bad bog. I think I would try to find out what the factory setting is for this and start there......