Okay, so the question isn't actually "how we're going to kill it". It's going to die when there's a better alternative. So the question is really, "What can we do to build a strong web-of-trust system while continuing to use the broken one?"
I see no reason we can't make some browser plugins, get some activism going in the tech community, and start building it. Just report back what cert was served to you.
With that being said, there needs to be a selling point other than building a better internet, otherwise no one will use this plugin. I think there is one, though, and that's security. When your browser comes across a cert that differs, alert the user. You might not get grandma to use it, but it's something.
There are issues with this. I want to anonymously report what cert a website serves me, rather than giving anyone curious my entire browsing history. And also poisoning. But the latter is fixed by using this both the existing CA model and the WoT.
So yes, there are some problems. But c'mon, it's 2015, let's fix this already.