Oh yeah, the church vans of my old summer camp days! (I had written those off for precisely the reason you state, this being a one-way move especially!)
To the above points too, I probably COULD move substantially all of everything I really would NEED, but between the mechanical state of the car (fine enough, but I do know it needs brake work and a couple other similar items for a fully-laden trek across the mountains @ 400 miles or so) and the potential of wanting to have a couple items that would be too big for sedan dimensions, the van seems like a decent option.
Truth be told, based on the rough prices I'm seeing for one-way rentals from DC-Cincinnati, it actually would not be too far off to just buy a one-way flight, load up my two suitcases with everything they will hold (under 100Lbs.), and then ship a couple big boxes via UPS and that would get me to the same outcome and price, maybe even less.