In case anyone is interested, here is what U-Haul says when you tell them you have an Explorer:
U-Haul has chosen not to rent behind this tow vehicle based on our history of excessive costs in defending lawsuits involving Ford Explorer towing combinations. This policy is not related to safety issues. This is an unusual circumstance for U-Haul – we have built our success for over 60 years by saying 'yes' to our customers. We apologize for any inconvenience this may cause and are committed to working with our customers to find alternative options to help with their move.
And then they suggest renting a truck instead.
Sidetrack - I really liked what I saw in Sweden (at least where I was in the northern part): Since there are hardly any pickup trucks over there, just about every gas station rented small trailers! My Swedish cousin said that about 75% of cars have hitches, so it's easy to hop over to the gas station and pick up a trailer for a few hours if you need to haul something bigger than you can fit in the trunk.
To address the OP's question, maybe Hertz or SunBelt? Probably more expensive, but they may not have the crazy restrictions like U-Haul does.