Not even the hard to find hardware websites are able to provide a clue on where such can be found. There are a number of corroded pieces outside; I'd like to find a source before I start trying to adjust the tension in the cables. Suggestions?
The world of aircraft construction uses drilled-head bolts to secure things that may otherwise vibrate loose or cannot accept a locking nut. I've used drilled head bolts with safety wire to secure a wooden propeller to the threaded hub.
In this application, it would appear that the cable passes through the length of the bolt and the threaded hole in the head would accept a set screw.
I'm inclined to agree that they items would have been custom made for the manufacturer, but that would not preclude having some made, especially in a small CNC shop.
It seems unlikely that they would have to be particularly strong (as in aircraft grade, or high carbon steel, or grade-8) and could even be done by a hobbyist. I have a "toy" lathe from Harbor Freight that would handle the 3/16" through hole and a "toy" milling machine from another source that would manage the set screw hole easily enough.
You could save a bit of labor by purchasing existing drilled head bolts, although those may be quite strong and difficult to machine.
Unless you already know that the manufacturer of the solar screens has gone out-of-business, how about showing photos to local installers to ask whether they recognize the manufacturer? If the hardware from this kind of install commonly gets corroded, they might already have a solution for replacement parts.
Or, the existing hardware might be salvageable if you can get them off in one piece with WD-40. Soak in something like vinegar or oxalic acid to clean up the corrosion, and then coat in something like bearing grease to protect from future corrosion.