Keep in mind in reading firearms laws, reports etc and etc. i have seen mentions of regions (don't remember where) where a shotgun with shells in a side saddle would be considered "loaded" because the ammo and gun are next to each other / can be made ready to fire quickly. Might have been NJ, or NYS or both?
On the east cost where you are I would think you are in a veritable minefield of firearms laws and pitfalls. Drive through NJ to get to NYS? I lived there, there are more ways to jack someone with a firearms felony there than I care to mention. One memorable case I read involved a person who had moved from texas with a M1 carbine, and another gun or two. Said person got in minor legal troubles and this gun and a few other tid bits that would not raise even an eyebrow in another state were translated into 7 felony charges.
If you do the research I think you are going to find this is a whole lot of trouble for a just how much benefit? You want to know that you are 100% in the clear everywhere you go due to the nature of the places you travel and their laws. Face it, you could be the victim of fate... say you get rear ended or your truck gets stolen and because of inattention to detail you are in violation somehow, now you may well be hit with a weapons charge. It's the nature of places like NJ, NYC, MD, DC. I have lived there and now live in the west, I am sure even a minor issue like this, if you are otherwise square would not amount to much in most of the western states, back east a whole other story.
Please also keep in mind that while I full support the right to carry, keep arms in one's vehicle etc, many, many persons will question why one feels the need to keep a long arm in their vehicle even if it's an accepted right to do so and legal to do so. The simple reason for this is we CCW, or carry arms shall we say for self DEFENSE.
Defense implies an emergent threat situation that must be met immediately to save your life or facilitate escape from the situation. It is difficult to construct terribly reality based situations (i.e. NOT end of the world, blah blah blah) where getting a shotgun out of your vehicle, loading it, and deploying it somehow meets with an emergent need for defense of your life as a civilian. In these sorts of situations, you having the time or get it out, load it and deploy it makes it seem not like defense at all, more like offense which, frankly is not the primary duty or reason why civilians are carrying arms.
Yes I know in most states one may use deadly force to protect the life of another or stop certain felonies. I get that, but again, first off, how likely is it ever that you are going to find yourself in some such situation? A situation where you know a felony is happening, or life is in danger, and you have time to get your gun, load it, and do something? What kind of thing are you thinking of getting involved in? An active shooter? Robbery?
Do you see how this sort of discussion makes it look a little like you are either looking for a gun fight or looking to overstep a bit? Even more so given the legal aspects and such given where you are and where you travel.