This is a tricky one, but a really cool question!
I definitely wouldn't give it to Ubuntu. I do like Ubuntu's ease of use, however they have plenty of funding behind them already due to Canonical.
Debian seems like an excellent choice, however they don't really have an "organisation" behind them, do they? I think it's just a group of people from around the world contributing. Don't get me wrong, that is fantastic, but when you're donating money, you want it to be properly organised.
Given the situation above, I think that rules out many popular distros.
What I think I would do, if it's an option (although I'm probably thinking too much into it!), is to start up a company/organisation that just constantly adds features and updates to many FOSS projects - the kernel being one of them. I think that would be pretty cool. That means everyone can benefit
Cheers
Jonny
Evorack