What then is the appropriate care to bring down an unmanned unattended object hovering over your property out of arms reach?
There is none. The proper legal remedy is to follow it "home" and sue the owner. You have no right to damage someone else's property, just because you feel like it, even if it's on your property. This is solidified in the case law around owned objects left on your property, such as someone illegally parking on your lawn. You aren't allowed to slash all 4 tires to ensure it's immobile until you can call a tow truck to haul it away.
Perhaps throwing small rocks at the drone, or turning a hose on it would be appropriate. Something to indicate it's unwanted, but causes little to no direct damage (though may cause a crash, which would cause more damage). Similar to a boot on a car, which causes no direct damage, but could damage the car if it's driven off, and could cause minor unintended damage, such as scratches on the wheels.