Did you ever get an answer to removing the plug on your ATV carburetor? I think I see a little hole there, just stick a strong pointy thing in and gently pry, it should come out. Or use a short wood screw, screw it in 1/4" and pull it out. Or drill a hole near one edge, then use a small screwdriver to pry it out. Drilling shouldn't damage anything, as when it goes thru the plug you'll feel the drill drop down, so then just stop. Done Johnson outboard carbs for years this way never a problem.
bellarmine's post in 2007 Yamaha Grizzly 350 carb mixture screw was marked as the answer