Therein lies the rub, doesn't it? The first thing to do is convince people that voting independent or libertarian (or for that matter for an outsider candidate such as Bernie Sanders in the Democratic Party primaries) isn't un-American or unpatriotic or whatever weird notions people have about not voting mainstream but their democratic right and an absolutely reasonable thing to do (perhaps the only reasonable thing in today's political environment).

I think it can be done. If you think of another notorious modern two-party system neither of the UK's dominant parties today existed before the 19th century. Given how fast opinions spread these days it should be possible to bring about significant change in a matter of years rather than decades. Think about how quickly movements like the Pirate Party became successful in some countries. That they declined just as quickly again in most of these countries can be mostly attributed to their own stupidity rather than systems that are inherently averse to change.