The ethanol content in the new fuel formulations just ruins the fuel pumps and metering diaphragms in 2 cycle carburetors. Using a carburetor cleaner on a running machine would harm these components as well as the neoprene type tips on the metering and mixture needles.
Using the 89-92 octane gasoline and the best oil mix with stabilizing additives you can afford, is highly recommended. Run the tank and carb dry when you aren't going to use it for a few weeks or longer will also help tremendously.
We are rebuilding small engine carburetors constantly. About every two years it seems for most machines. Most kits are about $12. If you're mechanically inclined, it's pretty straightforward. Your local shop guy should be able to do it in 1/2 hour.
Also, your screws being 'all the way open', do they have limiter caps on them? Most limit what the consumer can do to the adjustment (because of the EPA standards).