Green Board over Vapor Barrier?
If you're just worried about that particular area, buy a sheet of Densarmor to hang the top of the tub. It will require a "glaze coat" of joint compound to get it smooth to blend in with the rest of the rock, but being "paperless", mold won't grow on it (according to mfgr's claims). I doubt enough moisture would ever accumulate to actually deteriorate the Densarmor (as attested by the regular board that survived 30 yrs.).
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