Here’s a post from a while back with a ProMaster kitted out for karting:
Looks like it fits pretty decent. From my own van experiences, you don’t actually need that big of a van to fit a kart in, all the extra stuff is the tough part to squeeze it around. And if you don’t need to use the backseats for transporting humans, you can get away with a pretty small footprint and fit all you need.
Another note from my van is that I added a roof rack and a hitch rack, and once I figured out the proper way to organize everything, I actually didn’t need either to fit all my stuff inside the van. But having the roof and hitch racks do offer a lot more capability if you need it.