I took the original carpet out of my 64.5 convertible this year. I destroyed them when I took them off never imagining that I couldn't replace them.
Yes, they looked like a pop rivet, like a 'fish eye' shaped piece of clear/white plastic, on both sides of the belt hooks. Almost like a tiny button not much bigger around than the hole they go through.
I don't know how you could recarpet without replacing them.
It has only been a few months since I saw the originals so I might try to improvise with something.
They are not under any pull or stress, just keep the two hooks from separating.
Just thinking out loud, but a drop from a glue stick might be a start.