Looks like beating Grand just got a lot harder. Minor FF6 Advance spoiler.

There's no guarantee, though, that you even need to play the Melody of Finite before banishing him. Has Maxy shown any ability to physically cross between dimensions, other than to and from THIS PLANET?

True, he's extradimensional, and that's the part that's surpressed by the Melody. However, if he did have the ability to cross dimensions, that ability might well still be usable while mortal. Heck, Undimension works off the same principle, and mortals use that.