No problem at all, just give the location where the moon is at the Zenith and use the distance as the altitude.
> Reason this works for the ISS is because of the subsatellite point. It can receive GPS signals regardless of altitude above the Earth’s surface.
No, wether the object can actually receive GPS signals is completely irrelevant to wether its location can be described in the GPS coordinate system.
You could describe the location of the Sun in GPS coordinates too, the altitude value would just be very large.