A Patriot is a kamikaze drone, with a 150 km range and mach-2+ speed. I think you are vastly underestimating the difficulty of air intercept, but I wouldn’t dismiss the idea out of hand.
My first recourse would be to use a simple noise jammer (like we do against garage door and mobile phone IEDs) to cut off communications with its base, and maybe a low cost anti-radiation missile to attack the base. For a military drone, (not on sale at Amazon, yet) the simple counter-counter would be to have an autonomous mode when jamming is detected, which might be something as simple as a “take me home”, or “attack the jammer” routine.
I might prefer a shotgun over a 0.50 cal, for lots of obvious reasons, number 1 being fratricide. Unfortunately, the Geneva convention on the law of land warfare outlaws shotguns. I would claim that the law of land warfare does not apply to drones. Adding a shotgun to the armament of every rifle squad would be cheap, and would enhance morale in many ways as well as reducing the probability of a drone returning safely to base to a value indistinguishable from zero.
4 Ways to take down a drone:
https://www.youtube.com/watch?v=X27-2WDIZR0&t=216s
Number 4 is using trained eagles. I saw two hawk strikes on my bird feeder Tuesday during the pi-day blizzard. Very impressive critters, trust me.
“Unfortunately, the Geneva convention on the law of land warfare outlaws shotguns.”
It does no such thing.
L