Well, seeing that I am a physics major I should know but I am just starting the introductory classes so I will give it a whirl.
According to my book, there is a center of mass created by the earth and moon. This center of mass is dependent on the masses of the earth and the
moon. This means it is actually the center of mass of the earth-moon system that is affected by the sun's gravity.
"The center of mass of this system orbits the sun as if all the mass of the system were concentrated at that point." - Fundamentals of Physics 3rd
Edition, Halliday & Resnick
This should at least prove that the center of mass of the earth-moon system would change, since the moon would be losing mass. This should mean that
the moon would in fact move further away from the earth but that is just a guess. However, if that mass is merely transferred to the earth, I THINK
that it would balance out once the material from the moon is then placed on the earth, thus allowing the system its original center of mass.
Maybe this is just too basic or even parts are incorrect but I am pretty sure that answers some of your question.
EDIT: I am really tired so the moon may actually move toward the earth. If I find out, cause I am reading it right now, I will let you know...
[edit on 31-10-2008 by Unlimitedpossibilities]