I have no idea. I was thinking about it this weekend because I am always looking to leave MA.
My thoughts were:
1. Put them in locked gun cases in a car. This option is not great because sleeping will s*ck. Can't go to a hotel, cant go to a motel (could, but with so many boxes it might s*ck) ... NES said the best is to sleep at a rest stop in your car.
Have to deal with driving around NJ, it is a total pain.
2. If the collection is not that big, get gun boxes and ship them. At least the rifles. Handguns can be easily concealed in a locked guitar case. I have one, I can put roughly 15 handguns in it, 30 if I double stack them using 2 layers of foam.
Still have to deal with driving around NJ, but can at least stop at a hotel, no one will suspect of 2 or 3 guitar cases.
3. Locked cases to an every day moving company - in my opinion the worse option.
4. Depending on how many rifles you have, locked cases inside cardboard boxes. You can stop at a motel and unload 4 or 5 cardboard boxes into the room. I am sure no one will notice.
5. A specialized company. Not sure who, need to research.
I would be interested in whatever you find.