Scooping the entire volume inside of Saturn's orbit sounds like a HUGE effort just to get 20kg worth of antimatter. It really isn't that much energy, about equal to a 400 megaton bomb. A big boom to be sure, but not enough to launch a fleet of interstellar ships. At the Cold War peak, the US and Soviets had several tens of thousands of megatons worth of weapons deployed.

If you want to do some big engineering projects, why not just build an Orion-style ship powered by nuclear explosives? I'd bet you get a lot more bang for the buck.

Not that I fault NASA for funding some wacky studies here and there. It's always possible they'll find a way to strain dozens of cubic AU efficiently....