First, a name change. I don't see why they're called Ultra Galaxy. Like, it makes them sound like they're a spun off group from Team Galactic. Now maybe it makes sense in-story though even then I would find another way to get across the idea you want from the team's name, and remember you don't need to have "Team" in front of it as we've seen with the Aether Foundation and Macro Cosmos.
With what I'm about to suggest below, can I suggest a name theme that uses the word "Compass"? Not only does it work with Westing's name (could also name his executives after other directions or directional terms) but how you can work with the idea he's for guiding children:
For The Children: So, Westings thing is giving children more freedom while wanting to destroy the world... and he's an adult businessman (who has people in his company working for him knowing this). So, I imagine your idea came from satirizing the whole concept of the Pokemon games having the parents send out their children to have a region wide adventure capturing elemental monsters to battle them. Alright, let's work off that. Westing's surface motivation isn't children liberation, instead it's about encouraging children to go on a Pokemon journey and his business is one that provides children trainers with all the services they'll need. That immediately flips his rather sketchy surface goal to one that would be positively accepted (he could advertise to parents that a Pokemon journey would help their kids learn responsibility & gain life lessons, and with his company's services they'll be safe giving them ease of mind). This would also explain what his company does and how he's likely rich enough to do his ultimate goal, either he owns the Pokemon League or works closely with them and thus has hundreds if not thousands of sponsors and investors; while kids aren't charged for the services the kids are likely providing free entertainment which means merchandising deals as well as advertising paid services for adults (if you had Westing doing this long enough could have some NPCs mention when they were kids they were part of this program and have remained a long time customer even when they had to start paying, which would both show how far reaching Westing's reach and influence is).
For the Genocide: But now we gotta connect this to global genocide. Hm. Well, we already have him a fusion of Lysandre and Rose, how about we also add in a dollop of Ghetsis (and a sprinkle of Cyrus). Make Westing a perfectionist, maybe an eccentric one but still everything he does is fully planned with no expenses spared. He believes if you're going to do something you should put your all into it... and thus you should always be at 100% your best when your an adult. Kids he sees as being untapped potential and started his company to help kids grow up to reach this full potential as adults. Yet, all around him he sees grown men and woman not working as hard, not doing their best, and some even going out of their way to do worst! Even people who were once children that had used his services aren't using their full potential his services was supposed to help them unlock! And HOW DARE THEY! All the world's problems can easily be solved, diseases and misfortune eradicated, no one poor and hungry and depressed. And yet there's people who rather not do anything or, worse, make things worse cause they profit off it. This world is unsalvageable. If humanity wishes to wipe itself so be it, infact why not give it a helping hand? And thus Westing, having driven down a blackhole of despair and madness, decides to destroy humanity (and probably make himself a god to reshape the world how he envisions it should be).
Yes, Westing is indeed someone who thinks
this world is imperfect.
Champ's Involvement & Westing's Plans: Now, since you want this to be the World Champ, this probably won't be like a normal Pokemon game's league. It would be a World Tournament, or at least one is going on. Now this brings in the problem of how the player characters gets involved cause how does a kid from nowhere become a participant in a World Tournament where the best-of-the-best see who is the best-of-the-all? In that thought, maybe having a normal Pokemon League going on that the player participates in might not be a bad idea. Here's my thinking:
While top trainers are all having their own tournament running in the background, all regions participating in the World Tournament are each having their own special League Challenge. Any non-VIP trainer who beats their region's League & Elite Four would automatically be entered into the World Tournament's Championship Rounds.
So, that there should solve some of the problems of there being a World Champion even though something like that hasn't existed before and how would the player get involved with that.
Also, since you want the World Champion to use Legendaries, could have their being one VIP trainer (a new one made for the game) who many believe will win the title not only because of their skill but also because their team of Legendaries (now note they probably wouldn't have mascot Legendaries or ones considered one-of-kind. Think Bird Trio, Beast Trio, Regis, Eon Duo, Cresselia, Heatran, Swords of Justice, Forces of Nature, Kubfu family; not sure about Mythicals, maybe they could have one as their ace, maybe even a new one). Could even have on TV reports of this trainer defeating other well known trainers like Champions, Elite Four, and Frontier Brains/Battle Facility bosses to build them up.
So, how to now get them involved. Well, one easy way is for them to be working for Westing already, though that's just copying the Rose & Leon dynamic. So instead, he sees this Legendary using trainer as an opportunity to begin his grand scheme. I would make Westings plan be having a way to make Legendary Pokemon go out of control, make them unleash their full powerful which should be quite devastating. A simple hypnotic device isn't likely going to work on all Legendaries and might be broken out of, so instead Westing would use a virus that makes Legendaries go mad. He'll infect the Champion's Legendary team with the virus, they'll go crazy and likely kill everyone one (not only eliminating the Champion but also all the other powerful VIPs so they don't get in the way) and then the Legendaries would split to spread chaos (the virus will also make them want to seek out other Legendaries to infect them, and once infected the Legendaries have no interest in each other). And thus Westing will end all of humanity by having Legendaries, Pokemon who he sees as "perfect", unleash their full potential upon the world.