Renting sounds like a good idea, but I have found it difficult to find a company which will rent vehicles with hitches and permission to tow. Even if you find one which is okay for towing, it won't be set up with an electric brake controller, and thus may not be suitable.
The last time this came up, someone
did have a suggestion for a company which rents pickup trucks that you can use for towing... perphaps they have vans, too.
An E-150 isn't so much the E-350's smaller brother, as it is the lighter brother. I believe that the bodies are the same: although the longest version is likely not available in the E-150, and the one-ton sits higher off the ground, the width is the same and the interior height is the same. It sounds like the 12-passenger spec might be important, but if not, I would consider lighter versions (E-150 <strike>or E-250</strike>).
Edit notes:
The E-250 model is no longer offered... sorry for any confusion.
It appears from the
Ford specs that the Gross Combined Vehicle
Weight is limited by the drivetrain, so every extra pound of a Super Duty (E-350) or extended body detracts from the towing capacity. Even in the ideal case for an E-350 wagon with the 5.4 (the 3.73
axle ratio) the towing capacity is 7300 lbs minus all of the passenger and van cargo
weight. Realistically, this is not towing 7000 lb, but it should still have lots of capacity for the Casita!