Well, my problem was fixed--easily and simply. Alfred (66andBlue) guided me to the solution which was my next step anyway. Here's the issue, at least as it applied to me.
These reproductions come with what is called a "truss head" screw to tighten the clamp and hold it in position. However, what is supplied OEM with originals is what is called a "washer head" screw, or a "truss head washer" screw. This made all the difference in the world. If you are unfamiliar with these terms, photos are easy to find.
I had put off solving the problem for a bit, but yesterday was my final drive of the season, taking my car to storage in Northern Michigan for the winter. As I was preparing for the 3 hour 155 mile journey I realized I still had the "visor problem". So, I took the old screws out of the old visors, placed them in the new visors, and literally in a matter of seconds the problem was solved.
So: with the supplied new truss head screws, the visors flopped around, not holding position on their mount. Changing the screw to a washer head screw, and both visors were instantly returned to normal.
Shown are a couple of photos, generic, of examples of "washer head" and "truss head" screws. I believe that since the actual screw in question goes into a sheet metal clamp, the screw threads would be sheet metal, not wood or machine.
Now, as to other quality concerns: these replacements are very well made in my opinion. When I restored my car in 1999-2001, I bought OEM visors from MB at the then-ghastly price of $125 each. Note, at the time others were screaming loudly at this price, just as they were at $300 grill stars. These OEMS are not, in my opinion, well made or worthy of the price commanded. While the originals delivered on the car were so bad they had literally crumbled to dust (OK, they were abused and 31 years old), these OEM replacements are quite similar. On the driver's side, the part that snaps into the retainer fell apart after 12 years. The insides have hardened on both as the foam has deteriorated. There's just about 15,000 miles and 15 years since the restoration, but the car has led a charmed life since then. Stored for 6 months covered up; garaged during the season, and never left in the sun but for a display or car event. I would have hoped that these OEM replacements, even 15 years old, would have survived better. Most everything else replaced at that time has--including OEM, reproduction and restored original parts.