"So switch to bird shot. Figure just over 1.5 oz of lead bb shot in a 12 gauge 3" shell, that's ~80 pellets. Significantly more likely to hit, but at 200 feet, the .56 grams of a pellet is moving at roughly 600 fps between air resistance and gravity, which is just over 9 newtons (2 pounds) of kinetic energy hitting the drone."
This would be my choice for drone dropping. The shot does not need to have any kinetic energy, all the energy required comes from the high rpm rotor (think rpm of a cpu cooler fan but reduce the weight of the plastic to that of a 40mm fan then stretch out the blades several inches). An example of an item that successfully breaks this type of rotor if it makes contact is a a dry leaf. The slower the pellet is traveling when it reaches the elevation of the drone the more likely it is that contact will occur and therefore the drone will go down.
The "hover" on something as light as one of these quads is about a 10ft sphere in still air as the drone is constantly adjusting trying to hold position, over compensating, correcting again etc. The movement in that area would be so rapid and erratic than you can essentially think of the target in this case not as 20" but a 10ft sphere. And honestly, that is giving a first time pilot too much credit.
"Yeah, commercial drones are wimpy, but not /that/ wimpy."
Yes, actually they are. You literally can drop one flicking it with your finger. It isn't uncommon at all for a new pilot to have destroyed his new drone on the first flight. They generally come with your first set of replacement rotors and you quickly learn to keep a stock of them. The rest of the drone is usually a bit more durable. But if you break a rotor at 200ft the crash will destroy the rest of the drone.