DEA weapons have the same problem as AA guns, the further away the drone is the harder it is to shoot it down.
I wonder how much longer until directed energy weapons become viable anti-missile platforms on the level of Patriot or Russian/Chinese missile based systems? Seems like the power output and size are getting close. No clue how many shots such a system can make before it has to recharge, but if you get like 20 shots in short order that would be very impressive. I imagine both power and cooling are still difficult.
I think the best solution is to intercept them in the sky. Basically what the RAF did against V1s, except with another drone. You could also fly a drone at a specific altitude and use it in a ECW role.