UPDATE! I’ve inspected the underside of the machine and found a brittle leather pad (or at least bits of it) which appear to be the mechanism for stopping the keys at the proper distance from the platen:
As to where I’m going to find a replacement for this, I dunno. I suppose I could make one from heavy craft felt or something, but there are intermittent slots in the pad to allow some keys full travel, and I’d have to figure out which keys need the slots and i’d have to position the replacement very precisely. Man what a horrible design flaw in this otherwise extremely robust machine!