Thanks everyone for the comments.
I think if Capitol were to ever put a tool like this to use, it wouldn't be for salvaging complete vocal lines out songs, but to simply isolate particular overdubs here or there. I've tried this tool out on a few other songs -- the break in "Girl Don't Tell Me," Mike's bridge vocal on "Wouldn't It Be Nice" -- and have gotten very promising results. Maybe this use scenario could result in remixes of songs / albums that are held up by just a few missing multitrack stems.
Have you tried the piano and guitar solos from SDSN Rhonda?