Everytime I have rented from national there have been mini vans and suv's on the EA. In fact, I once thought I was going to be stuck with a minivan (they were blocking the other cars from view). But, I do agree with Robin, if you really want a mini van, you should book one and not rely on luck.
Just an FYI, we rented an Impala (a full size) and it accomodated luggage for 5 people in the trunk. The trunks are huge.