The real solution is a trailer. I inherited a light crossover SUV that's more than capable of towing a 5x10 trailer with a modest amount of weight. UHaul rents trailers for the occasional use ~$20/day, no mileage charge. I say occasional use because it takes effort to go and rent it, and UHaul builds them like brick shithouses so you'll actually get one that's easier to tow if you just buy one for a few k$. And a trailer has very little maintenance compared to getting another motor vehicle. I've started bringing a pallet or two and putting them down under whatever I get so I can just fork stuff off at home (and then in the case of stuff from big box stores, fork the rejects right back on to get returned).
These Kei trucks look neat, but I don't think they would actually solve many problems I have. A dump bed would be fantastic, but I could just bite the overpriced bullet and get a dump trailer, too. Like if it can't even carry 4x8 sheet goods then what is it actually good for?
Have been thinking about a roof rack for sheet goods. Can't see why it wouldn't work.