I think it'll fit but you may have to use a different tie down system depending on what tire size you have. I don't think 35" tires will fit. The U-Haul trailers use a over the tire net that ratchets tight. I've seen Jeeps on them that used more traditional frame ratchets. Also if the U-Haul computer says it won't fit then they won't rent to you. So you may have to tell them a different vehicle. Their computer says my 2000 Camaro SS won't fit but it fits fine it's just really low. My driveway slopes so I just park at the end and it's almost a level ramp.
When I relocated from FL to CO 4yrs ago, I used a flatbed Penske trailer for my 2dr wrangler with 35” tires. I used my own Mac tie down straps. Had a trailer tire blowout before dawn in BFE western KS and pulled my jeep off the trailer before the roadside assistance from Penske arrived (knowing that I wasnt supposed to have a vehicle with oversized tires.).