I think the most practical way to get this to work for us, though not without a down side, is to reverse the flow!
The thing could be built pretty much the same, but use the pipe in the lid as the intake. Duct it from one of the turnbuckle access ports (for those of us with campers that have such) using a flexible vent tubing such as is used to vent domestic clothes dryers. Anyone who has opened one of the access doors with the ceiling fan on knows there is plenty of air available through there. A square adapter would need to be fashioned.
Reverse the direction of the fan or if the camper is reasonably air-tight, perhaps the ceiling vent fan could draw air through the cooler - that might not work as the air resistance of the intake and pads might put too much load on the ceiling van causing overheating (or there might simply be too many places for hot outside air to leak in.) But one could certainly try this before purchasing and installing an internal fan.
Depending upon the volume of air pushed (or pulled) though the cooling pads, there might be a "spitting" problem. In the original design, any water droplets that fly off the pad are contained in the bucket. In the reverse flow design, those would be flung out onto the floor, seats cushions or cabinets. If there is only a small number of droplets this might not be a problem.
And in a small camper like mine, one would have a 5-gallon bucket inside the camper taking up space. [A really clever person could figure out a way to build a cooler into the space between the camper and the walls of the truck bed - that wasted space. A tube would need to be run to refill the water lost to the evaporative process, of course, and the ducting could be an engineering challenge, but what a slick deal that would be if it worked!]