I skimmed through the site. I didn’t see how they convince countries to have their beeches altered. I can understand the assumption that countries would be eager to receive something which will benefit them directly, but they also know that they are serving as a “commons” as well and may want compensation for that.
If they're altering the beaches for free, the countries would enjoy a portion of the common benefit without any cost. In fact, the new 'green' (literally and figuratively) beaches would probably be a greater tourist attraction, so if anything I'd expect it to be beneficial, plus secondary economic benefits from the work being done.
It would be such a great tourist attraction that flights to visit the green sand beaches would spike dramatically... the jet exhaust offsetting the CO2 absorption.