Education takes a generation or two to work even for simple things, and what you're asking for is deep and fundamental. Surely you have noticed by now that a good quarter of the US population views all forms of public education with hostility. Think also how long it has taken for obviously sensible ideas to catch on, and then consider the much greater difficulty of inculcating abstract moral and political concepts.
Radical changes in awareness (and self-awareness) would be a fine thing, but frankly I think most people know about climate change already; some of them refuse to believe it, some of them would just prefer not to believe it, and some of them just don't care. The more public service announcements you make, the more they'll be denounced as satanic/communist/whatever propaganda.
Honestly, if you really want an outbreak of radical self-awareness, cross your fingers, hire every young organic chemist you can find, and start producing industrial quantities of LSD. That is not a facetious suggestion; psychedelics yield unpredictable but powerful changes in consciousness and can have a lasting impact on perception and behavior precisely because they subvert standard epistemological filters.
A move toward genuine sense of responsibility toward others is something that often emerges out of the shared experience of disaster. Just as you can lead a horse to water but you can't make it drink, you can lead people towards enlightenment but you can't make them think. Experience is the great teacher. Since we'd obviously rather not use disaster as our classroom, it's incumbent on us to create experiences that are sufficiently meaningful to alter behavior.