No Dan, they did not, they rebuild the entire airplane, depending on the airframe and Cavilier model, only certain components were rebuilt. There were a lot of surplus, used parts and components on those airframes to include the later ones. The term "rebuilt" or factory new can only be affixed by the original airframe manufacturer although the military loosely throws that term around. I'm not sure how many had H tails but I'm sure they were probably the ones made from 1967 on.
Just curious the addition of the H-Tail.
Guessing it improved the handling for landing.
Any high speed benefit?