>>...He’s doing his first solo in a small Cessna and suddenly...
Pretty much everything in the US that goes over 18000' has a transponder. https://pilotinstitute.com/faa-transponder-requirements-explained/
At a minimum, if the guy flying the Cesna has filed a flight plan - and it was accepted, he or she is fine.
The simplest thing is to publish a NOTAM in which NJ. MOAs (military areas of operation) are prohibited*, at which point we can be pretty sure it's not 'some guy in a Cessna'.
*there's 'restricted' (fly over, get yelled at, maybe lose your license) and 'prohibited' (fly over, probable jail time)
Old guy trivia: NOTAM used to be 'notice to air men', now it's 'notice to air missions'.
All that said, all the 'spotting' videos show that these things are flying with collision avoidance lights on. For intelligence operations, wouldn't those be off?