You'll save yourself much trouble, worry, and inconvenience. Good luck, I hope everything works out fine with the move.
I had to tow a 4WD pickup from Des Moines to Phoenix with all 4 wheels on the ground, because it was too wide to get on a trailer. The problems involved were horrendous. Bad hitch, wrong truck, rotten weather, snow, ice, blizzards, and leaking tranny fluid. Then when we tried to get it back together......
I won't go into the details about when the hitch ball broke loose in Albuquerque.

Sometimes peace of mind may cost a litle bit more, but if you think about what can go wrong, it's cheap.
Just make sure to check over the tires on the trailer they give you, including frequent inflation checks.
My experience with U-Haul has made me quite cautious. Double check everything, before and often during.
Scott