As an anarchist who would welcome other anarchists - sadly, I doubt if that's a reliable recipe to stop climate change.
Limiting (hopefully stopping) climate change can be done under almost any political system... except perhaps dictatorial petro-states. However, it takes years of work to tranform the economy. Transport, heating, food production - many things must change. Perhaps the simplest individual choices are:
- going vegetarian (vegan if one knows enough to do the trick)
- avoidance of using fossil fueled personal vehicles
- improving home energy efficiency (especially in terms of heating)
- avoidance of air travel
- avoidance of heavy goods delivered from distant lands
The rest - creating infrastructure to produce energy cleanly and store sufficient quantities - are typically societal choices.
As for corals - I would start by preserving their biodiversity, sampling the genes of all coral and coral-related species and growing many of them in human-made habitats. If we're about to cause their extinction, it's our obligation to provide them life support until the environment has been fixed.
Also, I would consider genetically engineering corals to tolerate higher temperatures. Since I understand that this is their critical weakness, providing a solution could save ecosystems. If a solution is feasible, that is.
Corals reproduce sexually so a useful gene obtained from who knows where would spread among them (but slowly - because typical colonies grow bigger asexually). Also, I would keep in mind that this could have side effects.
As for tempeature - it will be rising for some time before things can be stopped. Short of geoengineering, nothing to be done but reduce emissions, adapt, and help others adapt. The predictable outcome - it will get worse for a long while before it starts getting any better.
Well, today they are actually in production, while 5 years ago they were in laboratories.