Planes are complicated and also leave a trail IMO (gas, hangar, mechanic maybe etc.). I will double check but I think plans have to be filed above 18,000 feet for both planes an helicopters and when you are using instruments. Sure you can try to fly illegally and not file but the airspace in the NE is crazy busy and NC is in flight path of both Westchester and LGA airports and even probably gets overflow from JFK on a busy day and you will be seen on radar. We know from past experience that Homeland Security is active in the area too and I have no idea what exactly their capabilities are in the air! We also know that DEA is active in/around Long Island Sound as drugs are brought in by water. I am sure there are other agencies active but these along with the Coast Guard make no attempt to hide their presence in the area along the coast.
There are any number of people in NC that have helicopters and use them daily and most probably fly below the level where plans have to be filed and fly line of sight. But I also think that if you plan your flight intending to use instuments then you have to file a plan. The weather situation this time of year is hard to predict with popcorn storms, overcast skies and lots of cloud cover and these situations might require instruments in order to fly safely. I'm not a pilot so these are just guesses/many assumptions on my part so suggest doing more research to see if this is doable.
All this being said, if someone stays below the filing level which I think is 18,000 ft using a tactic like nap-of-the-earth/flying under the radar and they pick a good weather day then perhaps its possible that FD ultimate revenge fantasy of dropping the brick or metal drum could be accomplished. IDK about the radar situation for aviation and homeland security but my guess is that given the proximity to NYC that radar nets over the tri state area are elaborate and quite sophisticated. So, I really wonder if its possible to truly 'fly below the radar/nap of earth it' in the tri state area? Need a pilot to answer that question!
But I also wonder who would risk their pilots license and prison to facilitate such a plan? Look at MT and the trashbin odyssey (and the many other things she most likely did) and she was charged with hindering/tampering and is looking at 10 years and not seeing her daughter grow up! MOO
For all the reasons you list about flying, I think it more likely JD was placed into a container with holes and dropped into either a main river or ocean by boat.
JMO