if things are bad already, just use: sockets, screwdrive, thin wires, toothbrush, carb cleaner spray and some elbow grease as proposed earlier. Or if one of the $15 carbs, just replace the thing, even if I know the good feeling after a successful repair!!
To avoid gumming you could use additives once or twice a year and maybe stabilizer in the fuel, but they will not work well on real debris and chunks of gum.