Hi Pagoda69, I also have a 68 390GT fastback, 4 speed AC car ( Late car, built July 18, 1968) That also has the heavy duty battery option. Do you have a build sheet for your car ? If so, what does it have under alternator in the upper right corner. Curious on what ampere alternator your car was built with.
BTW, Not 100% sure, but I was told by multiple "in the know" people, that the group 27 battery wasn't available till 69, and that my car took a HD version of the 24F battery. Makes sense as my car has a 24F size tray also.
Thank's John