With the huge area in the back of a ’63-’67 coupe, it is very tempting to let the kids sit back there or even squeeze a “so-called” adult in there when going somewhere short. However, this area has little support and was only designed with an idea of a minor amount of luggage. Putting a human body in there can easily weigh more than the floor can support and thus the floor can contact the frame cross member and vibrate incredibly, setting up a terrible racket inside.
To prevent that, I came up with two large rubber stoppers about 2″ diameter and about an inch high. I then prayed up the floor a bit from underneath to slide the stopper between the floor and the cross member. I spaced them equally across the gap between the two side frame rails. They held in by contact pressure and were there when I sold it about a year later, after driving it daily on typical city streets and roads.
The rubber prevents any vibration from being transmitted like there would be if you used something solid like wood or metal. The dip at the front of the floor to the storage areas provide support, as does the rear bulkhead wall. So only the center section needs the stoppers.
This can also be used in the convertibles and all ’68-82 cars if you haul heavy items like tool boxes in the back.