Hi AJ, Welcome to the site. I read this last night. Been through this in moving from Ca to Texas. My B250 came here on a Car Hauler I hired out of El Paso. It was under a Dollar a mile. This ended up being my best option, but I didn't have the 6500 tow capacity. Compare costs of both. Some Trailer sales around here do rent. U-Haul is not the only game in town. They suck IMHO.
So. I have a few observations. I am glad to hear the Dodge is the Turbo diesel. My Ram 1500 3.6 is only rated to tow 5000 pounds. If you have a 6500 lb tow capacity you should be OK. U-Haul trailers take a larger ball. Some U-Haul dealers in Ca. are very fussy about renting. They made me rent a Box truck with the trailer to tow a disabled S10 Blazer. So. Beware. Be a bummer to get to Ca, and not be able to rent the trailer. They may or may not ask what you are hauling. I am unsure what the load capacity of the U-Haul trailer is. My B250 is rated at 6400, probably around 5000 empty.
I mention weight because it matters. Guys load up and tow overweight all over without issue. But, if you are borderline on weight, with no safety factor, and one thing goes wrong...
My Nephew lost his Mach1 when a U-Haul Dealer failed to install the larger Ball on my Sister's Nissan Pathfinder, The trailer came off the hitch and flipped the entire Rig off the road over the side of Cajon Pass. Everyone was safe, but total loss of all the Vehicles. The Trailer probably was within weight. Was the Pathfinder enough tow Vehicle? Probably not... U-Haul was at fault. But If they weren't, an adjuster could have easily looked at the GCVWR, and if exceeded, denied the claim.
Be Safe and again