I've talked to a fried who works on these kinds of systems (ex-defense industry). He claims that the reports of the US having trouble jamming are pretty accurate.
Of course, when I asked him to elaborate he said "yeah, can't really tell you the specifics haha"
No need to to disrupt the transmitters on the balloon that are up-linking data to the satellites.
Simply overload the balloons' C&C receiver front-end, given the closer proximity of the shadowing aircraft.