If distance was acceptable you could use satellites. I think you need to escort your drone swarm into hostile territory using something like an F-35 so the whole package can penetrate as a unit.
You might even want the drones to fly behind using a wire-guided system so they can't be jammed.
Imagine the F-35 trailing a cable that spreads out to 1000 wires. It's basically just a way of giving one F-35 a thousand smart missiles that it could never fly itself.
The basic idea is used by MIRV ICBMS. You get the whole thing into enemy territory quickly and then launch more attacks than the defense can hope to counter.
1. Fly to the edge of enemy territory.
2. Launch your F-35 towards the enemy.
3. Launch 1000 drone missiles following the F-35 (maybe from a C-130)
4. Split off drone missiles in variable sized chunks according each target detected.
Just imagine an F-35 with a dozen F-22s vs an F-35 with 1,000 flying missiles behind it.