Too funny, I do argue with the Conspiracy people at times. I call them the hoax folks.
As other's have pointed out, you can't get them both in the same photo, but why not get them in 2? A nice exposure of the moon can me combined with your moon free milky way shot. Be as realistic as you want or as over the top. Maybe an 800mm moon, in a wide angle shot of the milky way?
Funny thing about the light from the moon being bright. Standing on the moon, the light from the Earth is 32X brighter on average, than the reflected light we see here from the moon. Why? The Earth is much bigger, and more reflective. Another moon hoax claim is that the shadows should be pitch black if there was only 1 source of light, the sun. But were 3 other light sources: The Earth, The moon's surface which often included mountains behind the photographer, and the photographer himself. (Big bright white space suit)