The Earthshine is usually a small fraction of the total light we receive from the Moon. But near new Moon the BS is very small and the DS starts to dominate – but at which phase?
Using Hans’ synthetic lunar-image code (based on Hapke 63 reflectances and thus UNDERestimating DS intensity and OVERestimating BS intensity for phases close to New) we get:

It seems the ES contributes 10% or more of the Moonlight at phases closer than 10 degrees to New Moon, and more than 1% at 30 degrees from new Moon.

Now, the SOLSTICE instrument in space has produced data for total lunar irradiance at angles all the way up to 180 (or is it just 170?) degrees from Full, so potentially they have data that contains 1% and more earthshine. The LRO data mentioned in Buratti et al 2010 does not cover to near New Moon. BBSO only gets out to 140 degrees or so (i.e. 40 from NM).

Due to the simplicity of the Hapke63 reflectance there is potential for a brighter ES and fainter BS near NM so that a larger fraction of the Moonshine is due to reflected earthshine. (the above is thus a lower limit on the fraction of Moonshine that is ES, in other words).

Is there potential for using LLAMAS data from SOLSTICE to do some clever work on Earthshine intensity?