Drop the bowl right on the bike first if you can, or try not to turn the carb upside down or shake it hard when taking it off the bike. If you are worried about paint or anything like that take precautions, It really wont bother original paint but spray paints and stuff like that fuel can damage it pretty easy.
its a 7/16" wrench to break the mainjet free which holds the bowl in place. Reason I say to do this is to see whats on the bottom of the bowl. If there is a alot of sediment/water/debis it will gather there and give you an idea of what's coming down the line out of the tank. I would think that a float that does not float would not cause an issue like this, it would just flood. but little bits of debris or even bad fuel will create havoc like that, get bouncing around and water droplets get sucked up the main, or debris. every time you grab the needle and twist it to try and re-tune you may break it free, think its good, run it again and have the same problem.