Voting a third party is not throwing your vote away. It’s actually often the best way to make your vote matter.

I strongly disagree with this.

Elections are simply a case of math. If you abstain from voting, write in some random name, or otherwise vote for a candidate who is statistically incapable of winning, then there are only still only two outcomes for your vote:

• In the best case scenario, like you're describing, your vote has no effect on the outcome and your 2nd place candidate happens to win anyway.
• In the worst case scenario, however, vote splitting leads to the well-documented phenomenon known as the spoiler effect. In which case the 3rd most popular candidate, who may not represent anything close to the will of the democratic plurality, will win.

Personally I always plan around the worst case scenario when making important decisions, and so I don't believe in the concept of the "protest vote". Especially since so little concrete information can be derived from "reading the tea leaves" of 3rd party votes. (A big part of your premise revolves around the idea that someone out there will somehow get whatever message you're trying to send by voting for a 3rd party candidate. And that's obviously a very indirect and abstract form of protest even in the best case scenario. )

Also I think it's a strech to attribute easily 20th century work reforms to 3rd parties as they exist today considering two points: (1) there was a radical shift in political power, generally towards progressivism, at that time and (2) it can be argued that many of these reforms could be attributed more to labor unions in general than any one political party.

Vote how you want, or not at all, but we can't escape math in the end. Statistically speaking, a protest vote is at best a benign waste of a vote and at worst the cause of undemocratic election outcomes via the spoiler effect. So I'll continue to recommend against it, and recommend for more democratic voting systems that are less prone to manipulation and spoilage.