Poggers. Had to do something else but yeah, when there's an interesting idea I like, I can really talk about it for a while. Now for Nazarick. And let's assume that the entire tomb is in some large barren forest, I guess. I think it would also be more interesting if I sort of made speed equalized. Like, not literally, but balanced it enough so that even the Floor Guardians can't just get blitz stomped by any remotely powerful OPM character. But obviously everything else stays the same, such as AP (which the Overlord characters obviously get dwarfed in).
Day 1 of it would be fairly similar to episode 1 of Overlord, in a sense. Where Ainz quickly realizes he's in another world. He'd learn about the surrounding land and modern society without much trouble, and would probably question if it was Earth for a moment, but would quickly dispel those beliefs after learning about Heroes and Monsters, let alone whenever he sees the world map. He would likely spend time learning about the OPM world in more detail, and, as you said, would use the guise of Momon, possibly with Narberal/Nabe as his companion, to become a Hero. I imagine him and Nabe would both be A-Class immediately, albeit on the low-end of it, with "Momon" being fairly higher than Nabe in that regard, but not by a large margin. Also as a side note, seeing as the OPM world is now pretty much confirmed to be a sort of futuristic version of Earth where all of the continents merged (but the common currency still appears to be Japanese Yen) and I also think the signs in OPM are all written in Japanese, I'm just gonna assume the written text is commonly or always in Japanese, which Ainz would quickly recognize and probably wonder about. He'd probably learn about the history of OPM's Earth, and wonder if he came back to the "real life" Earth, but for some reason went to a future version of it in the process. But of course, he'd also doubt that too, seeing as the OPM technology is probably not much more advanced than what his world's was like, seeing as Overlord takes place in the future, when nearly full dive VR tech is finally created. Overall, there could be many interesting things in regards to that. Anyways, Momon and Nabe would probably rise through the ranks of A-Class fairly high, but without the use of any magic (which they'd try to not use too much for obvious reasons, especially Momon), I don't think they could make it into S-Class. Their physical abilities are high enough to reach a bit upwards into A-Class, and if they use some tier 3 or lower magic on top of that I could see them getting close to the top 10. But even if they weren't as concerned about using magic as in the original series, they wouldn't want to overly stand out, at least not as much as S-Class Heroes, anyways.
Back in Nazarick, they would likely be using several spies to learn how powerful each S-Class Hero is, disregarding every Hero below Amai Mask as irrelevant fodder. They would also quickly begin to go out and capture Monster's, for experimental purposes and similar things. I could possibly see the intelligent researchers of Nazarick finding out how to use something similar to Monster Cell's, and slowly begin building up an army of Tiger, Demon, and maybe even lower level Dragon Monster's, although they obviously wouldn't want to make something too powerful, as they would understand how outclassed they are in terms of raw power when pit up against the more powerful denizens of the new world. After analyzing the S-Class Heroes enough, they would likely try to devise plans for dealing with all of them, mostly focusing on Child Emperor, Flashy Flash, Metal Knight, King, Tatsumaki, and Blast. I think they would be especially cautious of Metal Knight, Tatsumaki, and Blast, among that group. Metal Knight is mysterious, highly intelligent, and holds a vast arsenal of powerful equipment and machines, not to mention has a lot of influence over and throughout the Hero Association, however I wouldn't be surprised if Nazarick eventually tried to form some sort of alliance with him. If they ever deemed him as someone that could be manipulated or at least willing to work with them, they would obviously want his power, influences, and resources on their side. Tatsumaki is the Hero Nazarick would be most cautious of, and they would likely begin to devise plans for countering her immediately. Her raw power and ridiculous range make her one of the worst enemies for them to go up against, seeing as she could literally crush any of them into a fine paste instantly by just thinking about it, which is pretty much on par with Ainz's instant death hax, except she can do it on an incomparably wider area of effect. And of course, Blast they would be cautious of simply due to the fact that he's number 1, and rumored to be the strongest Hero around, thus making him potentially more of a threat than even Tatsumaki, but because of the fact that he doesn't even do anything anymore, they would still be more afraid of Tatsumaki. Seeing as the Heroes here are far more threatening than anything seen back in the world they were previously in, Nazarick wouldn't begin their plans of ruling the world nearly as fast. They would be very slow, very methodical, and would take extreme measures to be certain they're prepared for any event.
I doubt they would get involved in any of the major events at all, up until the Monster Association and Garou make their debut. However they would obviously keep track of anything major, such as the meteor, let alone the literal space pirates. Oh, and I forgot to mention it, but they would no doubt be even more interested in working with Metal Knight after learning that he collected the spaceship's material. It's also possible that they would notice Saitama's power, and keep an eye on him, as well. After hearing about Garou's feat's of fighting S-Class Heroes, as well as his motives, I find it very likely that they would also attempt to convince him on joining their group, but obviously Garou would decline. Depending on who asks him, it could potentially lead to a violent confrontation, but I doubt either side would have a casualty. When they learn about the Monster Association, the only organization in this world remotely similar to their own, they would either try to conquer it and seize control of its power, or would try to form an alliance with it. Although I think it's more likely that they would form an alliance, but while they would lend some aid during and before the raid, I doubt Nazarick would get heavily involved, still, it would be very interesting to see a talk between, say, Demiurge and Gyoro Gyoro, and I can only imagine how it would be. But again, they would not want to paint a target on their back, making themselves known by genuinely fighting against the S-Class, and also being weakened in the process is not something I would see Nazarick doing, and they would likely deem the Monster Association as foolish for believing themselves nigh-invincible. I also imagine The Organization is going to be something that could have an interesting dynamic with Nazarick, but I won't get into that since we know so little about them.
From here on I could only speculate about what could happen, because obviously OPM isn't finished, but when Nazarick does inevitably start their attempt at ruling the world, they would finally set a big plan in motion. They could probably manage to kill several weaker S-Class Heroes right off the bat and with no trouble. If they devise a good enough plan to deal with Tatsumaki, and manage to eliminate her, that's obviously one of the biggest hurdles dealt with. Assuming they managed to get Metal Knight working with them (whether through force or just convincing him some way), the only genuine threat by then is Blast. They would likely manage to either learn that King is weak, and would kill him while maintaining the bluff, to further demonstrate their power to the world anyways, or would kill him quickly in their plan, assuming that he was a powerful warrior, but that the plan successfully killed him before he could do anything. Flashy Flash would be a bit more troublesome, seeing as he's not just fast, but they likely wouldn't be able to keep track of him all the time. But he would likely be dealt with in time. Afterwards, it pretty much just comes down to Saitama and Blast. Blast would come out of hiding after all this time, realizing that a disaster level God has just shown its face, and well, we can only speculate whether he would be able to beat Nazarick or not, since we've only gotten a taste of his abilities. Saitama would certainly get into the fray when he realizes that so many people, let alone King, have been killed. And while his raw physical abilities are more than enough to deal with Nazarick if he was purely focused on that, I feel like Nazarick is smart and resourceful enough to have realized Saitama's true power by this point, and would have already devised a plan against even him. Assuming that even Saitama and Blast are defeated, then I can only assume Nazarick succeeds in ruling the world. Obviously God is still a thing, but like the Organization, we don't know enough about him for me to really say anything. And of course, the ending for the scenario here could also go completely differently. It depends on a lot of variables I don't want to go over, but yeah, if Nazarick makes even one mistake regarding some of the more powerful Heroes, it could result in their defeat.
My god I can really type for a long time, lmao.