Well, fascinatingly, the person over at MSE has posted a picture of the elusive Drummonds card!
It appears to be heavily based on the old “England and Wales” (to be Williams & Glyn) RBS design, and is really nothing special. I think I prefer the standard RBS Visa design that I’ve got.
However, they confirm that they are a personal customer and they are on the sort code 16-00-38, so the card is available to those customers. Although they say they had to request it at the branch, and some kind of criteria do seem to be applied. All very interesting.