The problem is you are trying to look at is as one giant entity doing this, when simply put that is very unlikely to be the case.Environmentalism or not, this is an engineering project, one of cost scale that i'm trying to convey here. It's way beyond the magnitude of any usual environmental initiative, period.
Largest environmentalist organizations operate with budgets of tens of millions $, not hundreds of billions. That's why "getting the ball rolling", getting some publicity and random people to donate a 2-3 digit sum makes a difference in the budget.
But it's a different scale of numbers we are working with here.
The costs of *not* doing that? Plenty of estimates of that too. The unfortunate thing is that the countries likely to take the brunt of that are those neither willing nor able to throw a lot of money at that.
I can say from experience that centralization of ecological engineering is unlikely to occur, and more likely you will see many small and medium sized groups coordinating efforts and sharing data/techniques. And some of these will be non-profits who are willing to eat costs to get stuff done.
What we need is more conservative voices and organizations among those groups, willing to bring a more practical mindset to the whole issue. Right now we barely have any voice in the issue at all.