Scooter tow arrived safe and sound.
As it turns out, shipping an 800 lb trailer 2111 miles is a lot more expensive than I had imagined. Still, even with the shipping, I have a functional Scooter Tow for a lot less (and a lot sooner) than it would have cost me to build one myself.
So after procuring a new battery, the scooter started right up. Next step, procure about 3000 feet of Spectra/Dyneema tow line.