If you try to rent a tow dolly from a national business (UHaul), they will ask what tow vehicle to tow what on the dolly. They will let you know if they will let you tow with their dolly. Now, if you give them incorrect information, you also sign a waiver and cost replacement document where if you were to be involved in a situation, you would be totally held liable for all costs and replacement. Even if you took their insurance on it.
Its the same thing with renting a box truck and trailer from them as well. You could look at loading the TJ into the box, put the JK on the trailer, and drive the truck across.
Yah, moving yourself sucks. Other option is to look into air fare costs. Leave something back with friends. Move yourself and family, get settled, then fly back on a cheap rate and drive back home. Vegas is usually not the expensive places to fly to. Many airlines have $99/$79 deals to get to Vegas. Another viable option is to let someone else you trust drive it following you. Hotel and food costs will be little more, but then you can use that person to also help unload your house as well. Then fly them back on a 1-way.
Have a friend that is doing just that. His wife took a job at the corporate level and had moved from KC to Pittsburg. She's flown back/forth for months. He drove out there with her WJ last trip and flew home. Next he's driving his daily with a pickup box trailer full of items movers wouldn't haul (propane, acetylene, gas cans (empty)). He'll fly back to get his toter, 22' trailer and Scrambler next trip. But that probably won't happen till they buy a house and he's got someplace to put it all. You should have seen the eyes of the packers when they were shown the working garage they had to pack. 20+yrs of tools, machine tools, small metal supply (big metal he's hauling with his trailer).
I moved out to KC from northern VA back some 12 yrs ago. I drove my Bronco pulling a popup camper. Flew back home, got my Cherokee pulling a small trailer of garage stuff (lived in townhouse so didn't have much in terms of machine tools). Then flew back home, closed on the house, moved wife, 2 small kids and a inlaws (lived with us) in a minivan. It was loaded.