As for all of the comments above aout transporting through various states, i.e. gun-unfriendly-Illinois, my (albeit limited) understanding of
18 USC 962A seems to indicate that it is Federally protected to cross state lines with firearms and ammo provided they are lawful in the origination and destinations sates while
in your vehicle and secured appropriately (gun cases, reasonably out of reach, another compartment if able, etc.). Even an overflight of Illinois and a diversion to a major airport with TSA on-scene should be entirely legal and perhaps some explanations as to the rules but ultimately safe passage should be awarded.
I'll state up front, I've not transported firearms by GA. When I was actively competing, I did transport quite a bit by commercial airlines, and I recently made a cross-country move which may be instructive.
One is
often protected by Federal law when moving firearms that are otherwise legal between two states where you can legally posses them. NY famously ignores the Firearms Owners Protection Act, and may arrest gun owners and confiscate firearms found being transported between residences. There have been threads on this board about it happening at the NYC airports, but in speaking with a NY firearms attorney he confirmed it has also happened to people driving through the state on an interstate move.
I had to research this early in 2024 as I was planning my own move from NJ to Idaho. I knew up front I'd need to rent a trailer to move the firearms, ammunition, and reloading components, plus a host of other things that movers won't take: any liquids, fire extinguishers, etc. Most bizarre: two big-name moving companies wouldn't take SCUBA tanks unless they had an official certification that they were empty. I noted that I'd removed the valves. Didn't matter, needed certification. I pointed out you could drop marbles in the tanks, you could look inside with a flashlight and see the bottom, you could poke a stick through the neck and into the tank. Didn't matter, no official certification that the tank was empty, no move. And neither company had any idea who would provide such a certification. But I digress...
Anyway, I knew I'd be towing a U-haul trailer for 2700 miles--not through NY, fortunately--so I had to do some research first. Most of the states on the route were either gun-friendly or at least gun-agnostic. Only NJ and IL are openly hostile, and I already knew NJ law pretty well. So I consulted an IL firearms attorney, who enthusiastically backed my plan to not take the direct route around Chicago. Stay out of northern Illinois entirely, he advised, they'll prosecute, and it would be a long, expensive, and not necessarily successful battle to prove that Federal law was on your side. He allowed that driving across the middle of the state was less likely to be problematic...law enforcement tended to me more reasonable and less political there...but if I chose to do so, do it non-stop. No overnight, no fuel or food or restroom stops until safely out of the state. Driving around the southern tip of Illinois would be the safer option.
So if you are avoiding airports with a TSA secure zone that you might find yourself in after an emergency landing, and if you are flying over
most any of the states, I'd say it can be done without issue. Flying over NY, NJ, MA, IL, CA, WA, OR would be cause for concern, especially if you were to find yourself on the ground in any county containing one of the main urban areas. Law enforcement in the more rural parts of those states tends to be more reasonable, but it can depend a lot on the particular officer with whom you may be interacting.
Good luck.
. I'd like to think you'd still be protected, but some police departments have been known to "hold" guns indefinitely. 
