Jubal:
I'm sure that most moving companies would be willing to move them, but I cannot think of any who I would trust to move them. Had a commander once who lost his entire collection to the movers. The company's insurance limit was reached pretty quickly. Although his personal insurance paid off, he was still looking for replacements two years later on some of the scarce or obsolete models. Don't know if he ever did find replacements for all of them.
You have to move the ammo yourself anyway, might as well make some room for the guns and family heirlooms as well.