Good thread, as I just bought a Street Glide less than a year ago. I checked the reciprocity map for New Hampshire and there are a lot of states that don't recognize your CCW permit. Yes, a lock box should ensure compliance but there are many states that will allow you to have a loaded pistol at your disposal on your bike. Texas will allow you to keep it in your saddlebag. New Mexico (my state) even allows anyone to carry concealed while riding. But as soon as you get off the bike you break the law. Big help huh? My point is that you should make use of the resources on this site and elsewhere to know the laws of the states you will be traveling through.
Another option is one I'm taking advantage of and that's to add a non-resident permit from another state to your wallet. I only need 1 more hour of classroom instruction to qualify for a Utah permit, and that with my permit allows me to carry concealed in most states in the US.
That's just my 2 cents FWIW. Anyway, stay safe and I envy you the chance to travel across the country on a Harley.
Jeff