I would call the local uhaul. They're usually privately owned. The one around here will do it. Not only did I have a soft top on my old jeep, but it wasn't even on when I went to rent a trailer , not to mention it was a 6x12 enclosed which I was pulling behind a 2 door TJ. Was all kinds of wrong, but I was just going a very short distance, kept to back roads and went slow.
Anyways, regardless of what the site says they will probably do it. If not, go to another one.
It's U-haul's corporate policy. You may find a local franchise willing to look the other way, but the paperwork will state a hard top is mandatory. If it's that big a deal, borrow a hard top for when you pick up the trailer, then swap it out for your soft top.
2012 Black JKUR...stock for now
This true I had the same experience when I went to reserve a small 4x6 to drive from Texas to Florida. Counter lady said no go I said I will drive my truck then. Showed up in buddy's f150 towed trailer to my place hooked up and hit the bricks... Figured what would they say in Florida return it to tx? Dropped off in jk with top down not a peep. Weird rule but I assure you it tows fine behind a soft top.
They also won't rent a trailer to you if you have a Ford Explorer, despite the current vehicle having the sum total of exactly nothing in common with the ones that caused the problems fifteen years ago.
Hold my beer and watch this.......
Call another rental company that rents lawn tractors they will have trailers you can rent.
2012 Sport Auto 3.73
ACE rock sliders, Warn M 8000 with synthetic rope
Eaton Trutrac Front and rear
17 inch ATX Ledge wheels on 285/70/17 Duratrac
Cheap is never a good thing when it comes to your Jeep