That guy’s system in the video is really slick, but in your case with only two inches of clearance from the truck body to the jacks this sounds like a recipe for paint damage or even denting your truck unless you have additional features to positively align the camper as it moves. This is based on my experience and difficulty precisely moving my Grandby on a conventional dolly with good quality 6 inch casters on a smooth concrete garage floor. It would be even more difficult on a rougher driveway surface. I would like to know what kind of casters that guy uses. I have way more difficulty pushing my camper on the dolly than he appears to have. I wonder if his camper is a shell with much lower weight than mine.
I would not attempt this unless I had guide boards in the bed of the truck that forced the camper to remain centered while sliding in. Even then I think you would get bound up and put high lateral loads on your jacks, which you want to avoid. Another approach would be to use tracks for the casters that can’t slip on the floor.
I built a track system for my dolly to load and unload the camper outside my garage door because the installed camper is 2 inches too tall for my eight foot door, and my driveway has a ramp up into the garage that my dolly can’t roll up and down safely. It’s a completely different approach but shows an inexpensive way to build tracks to guide the casters. The tracks are 2x10s laid flat with plywood strips making the sides of U channels on the 2x10s. I used 2x10s because my tracks are raised and span between support blocks. You could use 2x8s if they are flat on the floor. Getting the loaded dolly on and off you 1.5 inch high tracks to transition from moving around in the garage to on the tracks could be done with the camper jacks. If you blow up the picture you can see my tracks. Notice that I have cross members fixing the distance between the tracks.
Regarding your original question of how you can make a U-shaped dolly frame with adequate stiffness, I think you could achieve adequate stiffness as far as opening and closing the U with 2x8s laid flat and joined with large 3/4 inch plywood gussets at the rear corners taking advantage of the space under the truck behind the rear wheels. I’m thinking two 2 to three foot gussets, as allowed by the space under the truck. I don’t think there’s a practical way to achieve adequate torsional stiffness of the U for a lumber frame to resist twisting if it is loaded in twist. However, you don’t need torsional stiffness if you are using the frame only on a flat floor or driveway.
Such a dolly would be very unwieldy to store, so I would suggest attaching the major pieces with bolts so it can be easily disassembled for storage. That’s what I did with my trestle system. It takes me maybe 20 minutes to set up and 10 to tear down.
I’m a DIY person for everything except major surgery, and i know if one sets their mind to solving something a certain way they often need to follow their idea to a conclusion. (There are probably several episodes of the Red Green Show i could cite here but I won’t bother trying to identify them.). However, just speaking for me here, I would not try to solve the problem of difficulty loading this way. I think there is less risk to your truck and less effort involved in just taking your time and backing your truck carefully under a stationary jacked camper. If you are new to this it will get easier with practice. Get out and look as many times as you need to when backing. I’m getting pretty confident about it after four years but I still do a lot of getting out looking and several resets before finally backing all the way in.
I suggest getting jack extension brackets for your front jacks if you only have two inches of clearance. Four inch extensions should be plenty to reduce your stress and increase your margin for error. You can see my jack extensions in the picture as well. FWC dealers have them or you can make them from steel plate.
Consider applying your DIY skills to making guide boards for the truck bed to assist in loading the camper and to help keep it centered while driving. That’s a project I’m planning for this Spring when the camper goes on.
Good luck with whatever you decide to do, and keep asking questions if needed.