By the time you buy a vise, upper vise block, torque wrench, barrel nut wrench, anti galling compound and find a place to bolt down the vise, you could have been to and back from a gunsmith or armorer three times. If you try to rig something up, it's going to take even longer and there's a chance you will be making another trip to the LGS to buy a new upper receiver.
Go support your local smith and save yourself a lot of hassle doing it.
How about laying 2 short 2x6s on top each other like a step, lay a towel over them, lay your upper assembly with the hand tight barrel nut on top, and cover it with the towel. Now drive your car up on the lower. Tighten away.
USA Carry believes NH does not recognize a Utah non-resident license.
Handgunlaw.us states NH recognizes Utah, but does not specify resident vs. non-resident like USA Carry does.
I could not locate relevant information on the NH website.