Great article. We need to think before we waste our breath on the unpersuadable.
Kathryn Schultz's book "Being Wrong: Adventures in the Margin of Error" is the best thing I've seen written on this topic. She points out how we all think we believe things because they're true, and our brains are ill-equipped to process the possibility that we were wrong about the truth. So when we do change our beliefs, we have to rewrite our personal history (something we're quite good at) to convince ourselves we never really thought that other thing.
That's probably the key to persuasion. If we offer people a way to see the change not as an admission of error but as a reaffirmation of some other deeply held belief, they may end up acknowledging that they always did agree with us.
That's harder, of course, with people who have publicly committed themselves to a position, a candidate, a church, etc. and will lose large portions of their social identity if they renounce it.