Democracy will work, it's the only thing that's ever worked. Mass movements achieved pretty much anything you can think of, like better working hours, better rights for women, civil rights, end of slavery ...
Literally every (correct) example you gave is a case of people voting in their own short-term self interests, a dynamic which does not exist with global warming.
In the case of slavery, democracy didn't end this. Southern states literally seceded, and we had the bloodiest war in American history, to end slavery. And the dynamics there were that the economic systems of Northern states didn't rely on slavery, so they had little problem opposing it on moral grounds. The entire economic system of the South was built around the plantation system and slavery and so it's not surprising democracy didn't end slavery there.
The end of slavery in the United States was achieved by killing enough people who politically supported slavery in a war, that they surrendered and accepted the _de jure_ end of slavery. However, they then spent a century in a a low intensity conflict / rebellion (Reconstruction, Jim Crow, etc) against it, with significant success (unfortunately).
Democracy is not the cure all that you make it out to be.
In the case of slavery, democracy didn't end this. Southern states literally seceded, and we had the bloodiest war in American history, to end slavery. And the dynamics there were that the economic systems of Northern states didn't rely on slavery, so they had little problem opposing it on moral grounds. The entire economic system of the South was built around the plantation system and slavery and so it's not surprising democracy didn't end slavery there.