Well, Five pages late[r]...
- Malthus: Falsified
- The underlying problems? Money is not speech and corporations are not people. It shouldn't take money to fix that. Follow Lawrence Lessig.
- Energy: R.B.Fuller explained that an electrical grid intertie across the Bering Strait would allow the global shifting of solar input. In the 70s. Everyone has forgotten that, as well as World Game. In fact people keep reinventing that—and it is an ideal model for your 'science fair' idea.
So... saving the world without USD$1beelion: Put governance on the blockchain.
As Einstein pointed out, you can't solve problems with the level of thinking that created them. Ergo; all of humanities intellectation needs to be elevated simulatenously, that no-one be left behind. Bucky Fuller's Design Science revolution, that brings even the super-rich into a world they otherwise couldn't enter.
I'd always wondered how to crack that nut. It turns out you tie it to money. Specifically cryptocurrency. Making the bankers unemployed before the burger-flippers sucks 'em in, but then they get unassailable attestation and stock markets and voting systems as an unexpected bonus.