U-Haul gave me an estimate of $319 for installed hitch and wiring
harness, which isn't too bad.

However, my thought is that there must be old hitches out there on
cars no longer being used as tow vehicles and I might get one cheap.
I'll try calling junkyards next.

Go with U-Haul. The iron itself is not that big a deal, but the installation
is. Cutting
a hitch off an old wreck and then giving your neighbor a sixpack to weld it up
for you.....and then trying to wire it properly,
is a lot of work save a piddly $319.

The guys at U-Haul probably aren't rocket scientists, but they do specialize in
installing hitches and can probably do a better job on the 1751st hitch job
than you would do on your very first.

Considering the dollar value of the trailer and load, the hitch and the
installation is a poor place, IMO, to economize.