I am interested in how you came up with 0.6768. For a straight gamma 2.2, a pixel value of 127 would give a density of 0.6661 according to Bruce Lindbloom's companding calculator.
To calculate the density for a pixel value of 127 in a gamma 2.2 space, one would normalize the pixel value by dividing by 255 to get a value of 0.4980. For gamma 2.2, the pixel value would be 0.4980^2.2 = 0.2157. The density would be log (1.0/0.2157) = 0.6661, which is in accord with Bruce's calculation.
For sRGB one would have to use the inverse sRGB function. The normalized sRGB pixel value would again be 0.4980. In linear terms, the value would be ((0.4980+0.055)/(0.4980+1.055)*2.4 = 0.2122. The density would be log(1/0.2122) = 0.6732