The giant impact hypothesis for the origin of the Moon points to the creation of a hot, young Moon, likely with a global magma ocean. Such a magma ocean would produce a flotation crust of plagioclase crystals,or an anorthositic crust. Early calculations of the expected anorthosite content of the lunar highlands crust did not match initial measurements of Apollo samples, and more recently have not matched Clementine measurements or SELENE measurements, because they assumed interstitial melt would freeze. We consider a physical model of a magma ocean with an accumulating flotation lid, and find that significant escape of melt can take place for reasonable physical parameters and timescales of melt migration, even allowing for the inhibiting effect of plausible compaction viscosities. This model permits more nearly pure lunar anorthosites, consistent with observations. The model encounters some difficulty in explaining the expulsion of melt for the near-surface crust (up to five-kilometers’ depth) that presumably dominates the Apollo samples, suggesting that impact mixing and tidal heating are needed to explain the discrepancy