OK, I've now done this (put an Evora on a U-Haul trailer) and want to document some things here to help others who are considering doing the same. I apologize for not having detailed photos of how the car sat on the trailer, things were a bit rushed at the dealer. I do have some "overall" shots which I'll post once I'm home (I'm actually driving the car home the rest of the way now, typing this from a hotel room).
First: It does work. But you have to be careful, as described below.
There are three sizes of U-Haul "auto transporters" (their name for the all-four-wheels-off-the-ground trailers). They are differentiated by the max load they can accommodate. There is a 6000 pound, a 7000 pound, and a 7500 pound version and that rating is marked on at least one of the wheel fenders. Either the 7000 or the 7500 will work, but the 6000 is noticeably smaller. I haven't measured it but given how tight things were on the 7000# unit we had, I wouldn't even consider a 6000#.
Next, you need some 2x10 lumber, a circular saw, some screws, and a way to drive the screws (impact driver or drill motor). You will need to cut two pieces 18 inches long each, to act as standoffs in the trailer's "front" wheel wells. You'll also need to cut two pieces 30-36 inches long, and two pieces 18-24 inches long. These latter two sets are screwed together, one of each size, to create two "ramps" that the rear wheels of the towing vehicle must back onto. Finally, you need a couple of pieces perhaps 1-2 feet long each (whatever scrap you have left over from the above) to put under the trailer's own metal ramps.
Next up are four ratchet straps. I bought four new 1.25 inch wide straps. This is VITALLY important, as you'll soon see.
Finally, you need four old hand towels, like the ones you use at your bathroom sink. Not washcloths, but the next size up - about 1x2 feet minimum.
To get started, find a place to park the truck and trailer such that they are "headed uphill" a bit, or at least no less than level. Do NOT park them "headed downhill" because this will further increase the angle of the ramps, which puts the front splitter area at risk.
Next, drive the truck's rear wheels up onto the double-high ramps you built. Raising the rear axle of the truck lowers the rear end of the trailer, which reduces the ramp angle.
Now put the 18 inch long pieces in the wheel wells on the trailer. These are at the front of the trailer; they each have a six inch tall bracket for the tire to drive forward against and a metal rod that ends up "behind" that tire. The rod is a connection point for the webbing straps that go over the tire to secure the vehicle to the tire.
Finally, put the spare scrap pieces under the ramps to further reduce their angle. That front splitter is really, really low... do everything you can to reduce the ramp angle.
Now you're ready to begin. You will be BACKING the Evora onto the trailer. Take a few minutes to get comfortable with that, because you don't have a choice. First, the Evora is a mid-engine car so its weight is predominantly on its rear axle and you MUST have the majority of the weight at the FRONT of the trailer or you risk serious stability issues when towing. Second, the rear angle of departure is about twice the front angle of approach, and there's simply no way the front splitter area will clear the various bits of metal on the front of the trailer. You will be backing the car up those ramps, period.
Before you start, lay out the trailer's webbing straps along the wheel channels. You will drive the rear wheels over them, then pull them over the tops of the rear tires and ratchet them down using the ratchets on the front of the trailer.
Get everything lined up and have at least one, preferably two, spotters since you will not be able to see ANYTHING from within the car. Backing up the ramps is difficult but not impossible, but it must be done very, VERY slowly so you can stop before something gets damaged if your alignment is off. That's pretty tricky to do with a manual transmission. My technique was to use the hand brake as my only brake, leaving my feet to operate the throttle and clutch.
Ease up the ramps a few inches at a time. Have your spotters constantly check that you're parallel and centered. Once the rear tires get up on the trailer proper, centering is CRUCIAL. There is only a few inches of clearance and you want those evenly divided on either side. Take your time, and restart if you must. It's worth it to get it right.
Once all four tires on on the trailer, continue backing up until the rears reach those metal rods and the 2x10 you placed there. Now you must get the rear tires over those rods and on top of the 2x10's. Obviously you don't want to overdo it, so this is another time for the hand brake + feet technique.
With the 2x10's in place your rear diffuser will clear the trailer's tire stops with 1-2 inches to spare. I would stop and eyeball that to confirm before actually backing the car all the way, just in case the spacing is different on your car or trailer. That's actually good advice for this whole endeavor: Go slow and double check EVERYTHING.
Eventually you'll have the rear tires up against the tire stops. Set the hand break to hold the car in position, then confirm someone lowered the trailer's left fender and climb out via the passenger door. You cannot open the driver's door when the car is loaded backwards because the trailer fender on that side isn't hinged to rotate out of the way. Lock up the car, you won't be getting back in until it's time to unload it.
Now run the trailer's webbing straps over the tires and secure them using the trailer's ratchets. You will find it difficult to get them to lay properly on the tires, because the straps were not sized with the Evora's wide rear tires in mind. In fact, you will probably find that those webbing straps COME LOOSE during towing! Ours did, multiple times, and if we had done what U-Haul expects and rely on just those two straps to hold the car in place AND in alignment, it could have been a very bad day.
Fortunately, I had expected this and brought those ratchet straps and hand towels. Lay one hand towel through the bottommost spokes of each wheel. Then, for each wheel, hook the strap's hook (not the ratchet's hook, the STRAP's hook) around the inside edge of the wheel channel and pass the strap through the spokes and on top of the towel. The towel is there to prevent abrasion of the wheel by the strap. Hook the ratchet's hook to some solid part of the trailer that is far enough down the side of the trailer that the ratchet has NO POSSIBLE CHANCE of contacting the wheel or tire. Then cinch up the strap as usual and carefully but very securely manage the loose excess strap so it doesn't flap around and hit the car in any way.
Now go back and cinch up the trailer's own webbing straps. If you secured the ratchet straps well enough, they will have slightly compressed the rear tires and the webbing straps may now be loose.
Finally, remove all the ramps and risers that you made out of 2x10's (except those that the rear tires are sitting on) and you're ready to tow. When you are ready to unload, repeat the ramps and risers setup, remove all the straps and towels, climb in via the passenger door, and have spotters watch everything as you carefully drive forward off the trailer.
Let me re-emphasize: Those four ratchet straps are not optional. They are vital to your Evora's safety. U-Haul would have you rely on just securing the front-most tires with their webbing straps, but there is enough slop in that system to permit the (totally unsecured!) rear-most end of the car to move laterally quite a bit. Given the usual bouncing and jostling that happens on every road, you can pretty much guarantee the car will want to move around on the trailer. Your Evora will not enjoy that experience, and neither will you.
The four ratchet straps work because they absolutely tie the car down to the trailer in one place. It cannot move. Even if those straps failed for some reason, as long as you had two opposite corners the car should be solidly immobile. When the trailer's own straps came loose (repeatedly) we were not worried about the car moving - we were worried that the straps might fall under the trailer's own tires and get violently ripped off, possibly damaging the car in the process. We knew the car wasn't moving because the four ratchet straps had the wheels and tires bound securely to the trailer.
That's it for now. I'll post some photos when I get home. But the bottom line is Yes, you can use a U-Haul trailer to carry an Evora. Total cost was under $75 for one 24-hour period which saved me many thousands in California sales tax... and I didn't have to worry about some casual brokerage-assigned trucker doing whatever to my brand new Lotus.
More soon... thanks!