It isn't necessary for L values read with an eyedropper to be "true" L values, i.e., values you would get from a spectro. For linearization purposes, it is only necessary that the eyedropper L values have the same relationship to one another as the true L values.? You said it yourself in the OP: "As long as there is a maximum black patch and white patch, it seems these act as an internal standard for the image file."
John Isner