Thanks, but instead of NH snow cover, I'm wondering about the snow cover directly on the ASI. The MOSAIC scientist in the video blumenkraft posted says that snow quality (albedo, roughness, stratigraphy, crystal structure) has a huge effect on the atmosphere-ice interaction and melt season progression. I suspect that these relationships are only beginning to be understood and that the scientists need more time to collect and crunch data before reaching any conclusions about the current situation. Thus, there may not be an answer to my question at this time.
Snow cover characteristics on top of the ASI could be a missing factor in melt season variability that (in addition to weather, melt ponds, drift currents etc.) makes multi-month ASI prediction difficult. Stephan shared regressions a month or so ago that showed Extent and Volume in prior months have poor correlation with September minimums. Basically nil in May, weak in June. It isn't until July that knowing those values gets you much predictive skill about September.
Then again, Slater model and some other methods seem to do a halfway decent job of predicting Sept. minimums. The more I think about this the less I pretend to know!