The thing about the Moon is, it's not really the Sun's "opposite", at least not in this story.
The Moon has actually been pretty closely associated with the allies of Joyboy and Nika, not their enemies. The Kouzuki Clan's crest is a crescent moon. The Minks use the moon to transform into their Sulong forms. The little robots that Enel found on the moon seem pretty friendly and willing to help. The Moon is our friend.
The Moon is probably helping "light the night" until the Sun returns, metaphorically speaking. The Night itself is the enemy, not the Moon. The Moon just reflects the light of the Sun, and keeps it's memory alive.
This MIGHT be why that image of Blackbeard as a child crying at the moon exists. Even at night, he cannot escape the light. The Moon is "ruining" the perfect Night, by keeping a flicker of the Sun's light alive. Blackbeard is metaphorically (or literally) the Night, not the Moon.
The Moon is also a little odd in One Piece because...there's probably quite a few of them? There are most likely multiple "Moons", it's just that Oda's hid this fact from us.
The Ohara Orrery from Chapter 392 shows us that there are actually 6 "main" moons, with a few "mini-moons" around those, for a total of 10 celestial bodies rotating around the One Piece World.
Also, the chapter 1138 Mural shows us that there's at least 3 "moons". The main one with 3 "sparks" around it. And then 2 other moons, almost hidden in between the First and Second World texts.
Some people are speculating that these "moons" are actually "planets". And that the One Piece World is actually a Dyson Sphere, with a sun trapped at it's core. I don't know if I personally believe that, but it's worth mentioning.
Although, we have seen some proof that the One Piece World is actually hollow. There's been multiple mentions of a frozen underworld in the story, by characters like Brook. And we know there was some sort of underground mining operation down there, due to the 1138 Mural. So, chances are the One Piece World has been hollowed out. And if that's the case, it raises a question. What happened to all the rocks and debris that was originally down there?
Well...what if the One Piece's main "Moon" isn't ACTUALLY a moon at all? What if the Moon is actually the original core of the planet?
What if, due to the First World underground mining operation, the core of the planet was completely hollowed out, and all the "trash" rock they didn't need was used to create a new moon for the planet? To "rebalance" the planet, due to the shift in gravity. If the First World civilization was advanced enough to terraform this planet to their liking, they could also make themselves a artificial moon.
Chances are, by the end of the story, Luffy and the Strawhats are probably going to visit the core of the planet, and see what the First World left down there. Chances they will free someone or something that was left imprisoned down there. And if that happens, the planet will likely destabilize, meaning they'll have to do something to "rebalance" the planet once more. So, what if, by the end of the story, the Strawhats have to return the Moon to the core of the planet, where it originally came from.
Uniting the Moon and the World once more. Making it all...One Piece.
(You put the lime in the coconut...and drink it ALL up! It makes you feel better!)
It's a crazy thought, I know. And pretty much baseless. But, it would be a reason for the Moon to come back into the story in a big way, by the end. And it would make for a pretty epic, cosmic finale.
As for who the Moon God could actually be? (Which...I know I've taken my time actually getting here.). I'm going to throw out Law.
Law's iconic white hat, actually looks a odd amount like a "moon". With the "spots" being "craters". That could be enough of a hint for Oda to count as foreshadowing it.
Law's Op-Op powers are also suitably "godlike" in power. And, well, if you needed to cut the Moon to pieces and then put those pieces back into the center of the planet....his Fruit would work pretty well for that. The Immortality Surgery also hints at greater "godlike" powers. Plus, he's a ally of Luffy, so that fits with the other Moon references that I talked about before. I think he's as good of a candidate as any.
(Plus, there's a doctor who plays a heavy part in the Coconut song. See? It ALL fits together!)