Not a nut plate that you're looking for. There are oblong nylon plugs with a slot that allow you to screw the instrument cluster to the dash. They grab and hold the screw. They pop right into the steel of the dash, and when you take the screws out they usually crumble apart.
Yes, original dash pads had metal backing. The urethane dash pads sold by NPD (for '68) have a steel insert; the "premium vinyl wrapped dash pads" have a fiberglass core.
Vikki 1969 Goldenrod Yellow / black 400 convertible numbers matching