Welcome to the Forums and the world of Vintage Airstream ownership!
So sorry to hear about your problems getting your new acquisition home. The issue with the trailer lights and brakes isn't a surprise to those of us who have been around Vintage coaches to any great extent. Prior to about 1990, Airstream tended to utilize wiring schematics for the trailer umbilical cord that were not of the industry standard - - so when one of these coaches is attached to a tow vehicle wired to the modern industry standard all sorts of strange things can happen - - and when the hazards of prior owner modifications is added into the mix, it is uncommon to make a trip home with a newly acquired Vintage Airstream where some rewiring of the trailer to tow vehicle connector isn't required.
When you compare the two wiring patterns, it will be clear why the issues were present with the attempted tow. Correcting the Bargman connector wiring may improve your chances of finding an individual whom may be willing/able to assist you with the tow home.
One problem that you would have likely encountered with U-Haul is that their coupler ball would have been the wrong size -- your coach should have a 2 5/16" coupler while the U-Hauls typically have a 2" coupler ball welded to their hitches. Finding a rental tow vehicle is generally a difficult proposition, particularly when dealing with a larger trailer.
Good luck in finding a solution to your predicament!