So, either Carnuke was on a different mountain, or Carnuke is mistaken about the elevation at which he found it, or Google Earth's elevation of "Kuh-e Takht Soleyman" is over 4,000 feet off. Google Earth shows Mt. Everest being 28,189 feet, when actually it is 29,017. So Google Earth is 28 feet off there. But 4000 feet at "Mt. Soleiman"? I suspect that Carnuke's disovery is not on Mt. Soleiman. The closest mountain to Kuh-e Takht Soleyman that is at least 15,000 feet tall is "`Elm Kuh" (36 22' 27.65", 50 57' 38.78" E), which I believe is also known as Mt. Alam; Google Earth gives its highest elevation as 15,269 feet. But `Elm Kuh is almost 11 miles from Kuh-e Takht Soleyman. Here is a site that shows that the "Takht-e-Solaiman" is a range of mountains.
Carnuke's reference to "Soleiman" is thus probably to the *range*, not the particular peak. But there too, the only two mountains in the Takht-e-Solaiman range at least 15,300 feet tall are Alam and the north peak of the Khersan (which is directly connected to Alam on the north side). So it appears that Carnuke's discovery is actually on Mt. Alam/Khersan. If that conclusion is correct, then one should be able to run a contour line around the area at 13,120 feet, and come pretty close to it.