I have no Idea if this would work but, can you call rental places in D.C. and ask them if they have any vehicles that were already driven 1 way to your area that they need brought back?
Well prolly too late but I had a Chrysler Grand Voyager which is basically the same as the Grand Caravan. I was told I could fit a 8x4 sheet of plywood in it. While I never attempted it, we did pick up furniture (A couch I think) and had no problem.
Now I have a Ford F150...... hauling's not much of a problem and it's amazing how many calls I get from family to pick things up. My husband calls himself "Juan the Mulch Boy".