I get the concept but the fact is that you're much more likely to kill something if you directly aim at it with something that shoot projectiles travels in a somewhat straight line and can reach a ceiling higher than 500m. On ships with its limited space its a terrible idea. Its a much worse version of the Pom-Pom vs bofors 40mm debate which showed that more accurate and longer range AAA guns were much more effective than sheer volume of fire. On airfields you stand a better chance of making your own airbase inoperable with UXOs than hitting anything not to mention thats a lot of personel and munitions that could be hitting things with auto cannons instead.
Thing is you can reach the same volumes of fire delivered with conventional AAA only its much deadlier and effective at stopping enemy aircraft.
Although I like your reply and spirit, I have to ask, what weapon did you carry in the army/marines? I was an M60 gunner, and I can say that the farther away/faster a target is moving, the less chance you have of hitting it is going to be. When I took the top gun competition back in the late 1980's, I dropped the longest ranged target with a single round, and the pesky range officer, who was threatening to throw me off the range for using just 2-3 round bursts per target instead of the regulation 6-9 round bursts, when the target dropped, so did his jaw. I had no more problems with him telling me how to be an effective gunner after that. I tell you this because I want to establish my creds, so to speak. As an infantrymen, all our training targets were stationary, and so very easy to hit. Had that 1,000 m target been moving, even a little, one shot would not have been enough.
An aircraft, moving at speeds no automobile of the times could achieve on the roads of the day, is something of an acquired skill, in that shooting at something moving at those speeds is not a skill one can get hunting small/big game, and adding in the three dimensional aspect makes this even harder, and so such skills can only really start accruing to those in the military, using military weapons, and if one is to hit an aircraft target, one really needs to be shooting at an airborne target, and unfortunately, a towed target is not moving in the same manner as an attacking aircraft is going to be. So the answer?
Augment your line of sight weapons with area denial fire, because you don't need to be able to hit the target if you flood the volume of space they have to transit with a barrage of scattering bomblets, from multiple mortars/launchers.
I'm sorry that I once again didn't make the timeframe clear in the OP, but then again I didn't even give the ranges of the desired weapons. For directly overhead, say a range of 1,000 to 5,000 yards for the bursting charge, and the scattering bomblets should scatter from 100 to 300 yards before detonation, and again, this weapon would be used in numbers, say 10 or more, so you have a large number of bomblets detonation within the targeted volume.