You were right that plurality voting is broken. You were sold the wrong fix. Here's what the data actually shows—starting with a chart that should settle this.
In 2012, researchers conducted an exit poll at Occupy Wall Street using four simultaneous voting methods: plurality (the current system), ranked choice voting, approval voting, and score voting. Same voters, same candidates, same moment. Only the counting method changed.
Approval voting = check every candidate you find acceptable. Score voting = rate each on a scale. Both explained fully below—for now, just look at what they do to third-party support.