You respect and even admire Godzilla for his abilities, but you're not a damn idiot! When Godzilla comes to kick ass, he goes into overkill. You don't want to be anywhere on the island when he arrives. You ask Moreau for your money.

"Alright Moreau, you said I could have my reward in cash, I'll be taking it now seeing as my work here is done."
"What?! You haven't done anything!" Moreau says.
"The hell I didn't, I got Godzilla to come here. He'll solve your Martian problem."
"Okay there's two things wrong with that statement. First of all YOU still aren't personally doing anything. Second of all Godzilla is Gil's cousin not yours, if anything he gets credit for this before you!"
"Yeah!" Gil remarks.
"That may be, but I'm the one who convinced Godzilla to come here! Gil was too busy stuttering and apologizing."
"Godzilla's not even here yet! I'm not paying you anything; you can wait until after he gets rid of the Martians."

Looks like Moreau isn't parting with anything until after the job is completed, but if you wait until after Godzilla does his thing there won't be anything left on the island to part with and that's assuming you can find some place to lay low to avoid the sheer destruction that's sure to come. (Even though Moreau seems to be ignorant of what's about to occur to his Utopia)

You leave without getting paid

You don't even care about the money or anything at this point, you just need to get off this island and Moreau's the only one who can fly the plane.

"Alright look, forget the money, just take me home, I just don't want to be on this island any longer the whole place sickens my sensibilities."

Moreau looks annoyed by your comment.

"Hmm, well if you hate my Utopia so much, I certainly won't keep you any longer. I'll fly you home immediately. I didn't want your kind really living here anyway. At least Gil is civilized enough to appreciate this place."
"Uh actually I'd like to go back to the mainland as well. I don't care about any money either, I'm not going to be living anywhere that requires rent anyway." Gil says nervously.
"What? I thought you wanted to stay?"
"I changed my mind! Can we just leave?!"
"Alright fine, I'll fly you both back. I'll get the plane ready. I'm a little puzzled by all this, you've helped me, but now you don't want any reward. All I can say is thanks I guess."

After Moreau leaves to start up the plane, you ask Gil what's up with him.

"So why are you leaving?" you ask.
"Duh! The same reason you are, because my cousin will destroy this fucking place, even though Moreau seems to be oblivious of that fact. Not to mention he still sounded pissed at me on the phone, so I don't want to be here when he arrives! (Sigh) And I did so want to live here too."
"Well if it wasn't your cousin, it would've been the Martians so you would've had to leave anyway. I'm not getting anything out of this either; I gotta go back to my cabin in the woods and figure out how to raise some money again. I hope Erik's got something lined up."
"At least you have a home to return to, I gotta find a new one all over again."
"Hm, well there's a small lake in the woods I live in, you might try that for awhile. Not too many people go into the woods, especially since I tend to discourage it."
"I might just do that since I don't have any better ideas right now, I guess you're not a bad sort for a land dweller. Sounds like Moreau got the plane working, let's get the hell out of here."

You and Gil proceed to talk about a great many of things while on the plane and become quite friendly with each other. Probably a first for the both of you. After Moreau drops you both off, you continue to discuss the old days while Gil checks out the lake you were talking about. He mentions it's a good place as long as nobody bothers him. Gil becomes your new neighbor and you both part ways since you both still want your solitude. You do get together to watch TV when a news story comes on a couple days after you left Moreau's island...

The Martians arrived just like they said, and so did Godzilla. A massive fight broke out, but of course the only winner could ever be Godzilla. Their flying saucers were incinerated by his radioactive breath and their troops were crushed underfoot with ease.

The entire island was also incinerated and crushed underfoot with ease! Most of Moreau's citizens were killed in the cross fire of this battle. Dr. Moreau was found dead from a self-inflicted beam blast to the head (A weapon he picked up from a dead Martian no doubt) Some of the survivors claim his last words were "Such destruction… Why? Why? Why didn't they tell me?!"

This massive devastation continued even after Godzilla killed all the Martians, apparently from some of the other survivor reports, he was tearing the place apart searching the entire island for something or someone. When he didn't find it, he gave a roar and went back to Japan.

After watching the news report, you turn to Gil.

"Alright Gil what the hell did you do to your cousin? I mean what possibly could you've done to piss him off so bad? It's not like you're Rodan or Mothra."
"Eh, it's not something I like to talk about Wolf. I'm not too proud of doing it, but…"
"But what Gil? Out with it!"
"Well…I kind of…impregnated his wife…I know what your next question is, and it's a bit complicated so I won't try to explain, but we aquatics mate a little differently than…"
"Alright Gil! I don't need to hear anymore!" you say, and then sudden you have to ask…
"So wait a minute. You mean to say Minya was…"
"Yep, he was my son. Why else would he blow smoke rings instead of radioactive fire and be so small?"
"Well I thought it was because he was young."
"You probably haven't kept up with Minya, but he's STILL that size and still can't breathe radioactive fire. My cousin knew something was rotten around Minya's 10th birthday, since he should've grown a lot bigger by then as well as the fire stuff. His wife confessed everything. It's another reason why I'm so reclusive."

You just stare in disbelief at all this. Even with all the dirty secrets you've known about in this business, this one is definitely a new one for you. You don't think you'll be able to look at Godzilla OR Gil in the same light ever again.

Godzilla might be King of the Monsters, but you have to give some sort of props to someone who fucked his wife and got away with it.