I don't understand why the USA doesn't use preferential voting like Australia does: https://www.chickennation.com/voting/
Instead of just picking one candidate/party, you number them based on your preferences. First all the #1 votes are counted. If no party gets the majority (over 50%) of votes, the party with the least number of votes is removed, and for everyone that voted for them, their #2 votes are used. Repeat until someone wins.
Independents (what you call "third-party" in the USA) can win, and any party that gets over 4% of the #1 votes gets election funding from the government (a fixed amount per vote).