I feel like it's only possible to come across as heavy handed if the satire is objectively less subtle than reality. In a world where climate science has shown us our future for decades now and people continue to bury their head in the sand, it's really just documentary about what would genuinely happen if a large scale disaster were to occur. I wouldn't say it's a particularly clever metaphor, but I think you can't satirize climate change denial hard enough at this point.