OK, I didn't go to the hospital after all today. My son's wife went instead, which was much better for getting questions answered.
The answer was, they didn't know anything about issuing of Green Cards, and all that I would need is to take my A5 sized appointment card everywhere, which is impractical i.e. to preserve it, it will need laminating, making it very bulky.
This is obviously going to drag on for a while, if it happens at all. As such, when I get back from my lake walk, I will do as sateeb requested yesterday, and give it a thread of its own. It looks as if somebody at the yop has said, "Make it so," but it isn't an easy fix for the plebs to resolve.
As for Mor Phrom, they confirmed it isn't working properly, so it's use is limited (there's a surprise).
My daughter-in-law also requested a Covid Passport in case I wanted to fly at some point, and they told her I needed to produce evidence of flying first
