I seriously doubt you'll fit all that in a "full size" rental. First, full size cars just aren't what they used to be anyway. And second, a "full size" car at most rental agencies is not the largest car they rent - those are often referred to as Preimum or Luxury.
As far as vans go, check at Dollar. They often have codes offering a van for $199/week. Look at
www.mousesavers.com for a list of current codes.