I think the likely need for my guns while traveling through a state is small, the use of them when stored according to FOPA slow and inefficient, and the instant I touch the gun I've shed my FOPA protection. The unlikely event of having to explain the gun is more likely than the unlikely event of my being able to use the gun to any purpose. So I would choose to forget the whole situation and ship them.
But that's just me. You're certainly legal to do it, and there's no reason you shouldn't if that's your choice!
The reason I would choose to bring them in the trunk rather than ship them (aside from cost and hassle of shipping) is the great unknown. If my vehicle breaks down in the middle of nowhere, even if that was somewhere in NY or NJ, a gun could still get me out of a mess. I might be risking a few felonies, but if it's me and my loved ones lives or my spotless criminal record on the line, family comes first. I can think of hundreds of scenarios where one could get stranded, scared, thrust into a natural disaster or something else where a gun a few seconds away in a locked case would be much better than a gun hundreds of miles away on a FedEx airplane.
But I will also respect your decision to excercise your rights however you see fit.