Interesting design. Sad thing is that I suspect that for what he would spend in a couple of years on gas he could afford to buy several replacement truck of the more typical variety. After filling up such a beast I would be welcoming a tornado to take me away from my suffering.
Considering the options I concluded that there may be no practical tornado-proof truck.
Of course most of us aren't going to be chasing tornadoes. So combining protection and mobility wouldn't be necessary. Instead the issue would be how to protect your vehicle while it is parked where it normally is.
What you need for this would be a tornado resistant revetment. For a quick thumbnail design I would start with a concrete slab or dual track-way. then an anchoring system. Helix anchors, commonly used to hold down mobile homes, if I didn't have a heavy enough slab. Poured-in anchors if I did. Placement would be designed around the vehicle. I'm thinking fore and aft of each tire so you could use over-tire nylon hold-downs commonly used to ship vehicles.
Once the anchor system is set up I would build three walls at least as high as the vehicle roof with just enough space between them for teh vehicle and to open the doors on one side. Railroad ties or landscape ties would be good. As would surface bonded concrete block construction. Once built gravel would be pushed up around these walls to provide mass and drainage. Then a layer of landscaping fabric to keep the gravel open and a finishing cover of soil, possibly terraced, to hold grass or other ground cover.
The revetment should be a bit long so the fourth half height embankment can have a slope on both sides so you can drive into it. And to allow some room to work under the hood.
The plan would be to make this your normal parking spot. In normal use the revetment gives you pretty good protection from uplift and wind-blown debris. If it is known that a storm of event is likely you would install the hold-downs over the wheels.
Building one it wouldn't be much more difficult, with tools and materials on site, to extend the revetment ten or fifteen feet and to install some overhead cover, a sturdy door inside the shelter and a hardened door outside. This would be a shelter for people and supplies.
The roof could be a simple 5V heavily reinforced for uplift just to keep the rain off. Or a more substantial model of reinforced concrete capable of surviving harsher conditions and protecting the inhabitants from various dangers.
And just as son as I have the appropriate land and excess cash rattling around my pocket I will be sure to build one.