FOPA 86 should protect you
SHOULD. You are transiting and the guns are legal where you came from, and where you are going. This was one of the big parts of the Firearms Owner Protection Act. However, this does not mean that local cops will not make your life hell if they catch you stopped in their state with the guns. Untimately a court should find in your favor, but until that happens, you could spend time in jail. It has happened to others. One fellow had it happen to him, because of the airlines. Others have had cars break down, or been caught in traffic stops. Fed Law says as long as the guns are unloaded, locked in cases (or cased in locked trunk) and legal where you are going, the states inbetween are not supposed to arrest you. But it has happened.
Shipping from a dealer to a dealer is safest, but costly. Cheaper than fighting a bogus state charge though.
Are you moving your houshold goods? If I was, I would just disassemble the guns, pack them in several seperate boxes in my household goods, and let the movers load them into the truck. Nor would I point out to them that there were guns involved. It is none of their business, and if they are not travelling with your person, then if you get stopped in NY or NJ, they have nothing on you. After all, when is the last time you heard of the cops searching the Mayflower van because they were speeding?
remember, if you plan to ship from an FFL to an FFL, not only will the guns be logged in their books (and possibly registered in their states), but the shipping FFL will need a copy of the recieving FFL's license, signed in ink (copy must be signed, it cannot be a signed photocopy), before he can ship the pistols. It is also possible the recieving dealer may have to do a background check on you before he can release your pistols to you. Maybe not, but I have heard some places require this nowdays.
I went through this in 2003, between NY and WA. Cost me $80 to insure and ship 3 pistols, with the dealer "doing me a favor" by only charging me for one pistol (since they were in the same box). Took about a month before the pistols were delivered to my FFL in WA. Might be faster for you , but I bet it will still take a few weeks!
Good luck.