I think the car may be a '78...but one that has undergone extensive rebuilding, including replacement of many if not most interior parts from earlier models. I have a gut feeling too, (which I cannot verify without seeing the car in person), that this car may have been involved in a fire at some time.
The only part that seems in sync with being a '78 however, is the black emergency brake handle. The distributor is indicitive of one used in a late '77 and up...and it's possible that this is the original engine too. However, the radiator set up and style is clearly that of a 75 or 76...a closer look of the stampings on it's upper corner would be more proof positive, as would finding the vin somewhere on the chassis. It has a later syle or replacement ignition module, and '76 style orange needle 120mph speedometer...the gauges probably individually changed into a 77 or later dash piece with the black plastic rings around them as opposed to the earlier chrome ones.
While its possible too that it may be a King Cobra, this would always be subject to question and a lower resale value, without the buck tag verification to prove it. Clearly, the restorer added ornamentation and an air cleaner housing that were not original equiptment....(unknowingly?) along with a spare wheel center that doesn't match the other four, that are also incorrect on a true King Cobra.
The interior has clearly had a redo, with seats and door panels likely coming from other cars as many have pointed out. The photo showing the rear cargo panels shows too much variation in condition and color to the rest of the interior, to make one believe something hasn't been changed.
I believe the car did have factory A/C, as evidenced by the lines on the front radiator support area...whether or not the engine with it's bracketry for it is original or not. The dash heater control unit appears to indicate the car had A/C too.
I question why the restorer did not replace the underhood braces for the T tops. It only raises the question too, of why the were removed in the first place. The bottom line? There's more here to "disbelieve " about the "authenticity" of this car being a true King, that what is being substansiated.