Trunk hardware

There were only two tire sizes for '67 Barracuda 6.95, and D70.
The 1970 Hamtramck Registry - 1967 Plymouth Salesman's Pocket Guide

A 6.95-14 has 7" section width and about 25.5" diameter. (when on a 5" rim)*
A D70-14 was 7.85" section width and also around 25.5" dia depending on tread.**
The E78-14 currently in my Barrcuda's tire well has a section width of 7.65 if it was mounted on a 51/2 J or JJ rim (which its not).
But its probably safe to conclude even the D70-14 tires never sat flush to the floor pan in this car. My car prob came with the 6.95, I'd have to check the build sheet, and those probably do sit flush. A C78 or a D78 would be pretty close and choice would depend on load range needed.

* Barry's Tire Tech
**Barry's Tire Tech