Rental car agencies will not allow you to tow anything with their vehicles, I actually looked into this to try and make my recent boat purchase easier to get it back east. I talked to avis, Hertz, and enterprise, no dice. So I had to make he drive myself (and I am still on it and posting this from my wife's phone!) New Jersey to Utah and back! ( yeah I know its a long haul)
U-Haul does in town rentals for pickups and vans, you might be able to score there. You don't know anyone else with with truck you can swap with?