Hasinoff et al have (link) shown how images of the DS edge can be used to invert for the illuminating light field (i.e. earthshine) and receive low-resolution maps of terrestrial albedo distribution.The pdf file is here:

Some notes on this:

1) The edge pixels that can be observed from Earth are differently illuminated because the source of light is extended and at a slight angle with the observer’s position.

2) Sally Langford described a method to find the edge of the lunar disk by using the Laplacian operator on the image and in essence do edge-detection. This method will be influenced by the fact that the edge is not uniformly lit. This applies, in principle, to our edge-fitting method too – except we have so low resolution that only 1-2 pixels at the edge show the effect. We do fit these – perhaps we should not.

3) We should be able to test the method Hasinoff et al describe from purely archival images found on the net – or we could try to get our own images (with the eyepiece projection method it should be possible to get high-magnification images of the DS edge). Or with the help of some willing amateur astronomer.
Or by applying for ‘service time observations’ at some large telescope.