All is not lost!
I am not sure when you are leaving, but the way that I see it, if you take the southern route (I-40?) all of the states that you travel through, with the exception of NV and WY, will recognize your permit.
More importantly, if you can quickly apply for a non-resident PA license, you will also be covered in WY. The cost is $31, and the approval time seems to be less than a month, as opposed to the NH license, which seems to be taking much longer to process.
In fact, if you call the Adam's County (PA) sheriff's department and explain your situation, along with providing the relevant documents from NC, I am sure that they would consider expediting your application. They are a really nice group of folks ( I used to live in Gettysburg).
That would leave only NV, and open carry is legal there, although I would be careful while in Las Vegas (or anywhere in Clarke County). Incidentally, NV requirements allow non-resident permits, but the training class for the permit must be done in-state by a trainer recognized by NV. You might consider taking a class while there. It would also allow you to carry in MN, should you go there.