Correct! (Was it that obvious?)
6,000 km/s is cooking. That's 2% of c!
You mentioned our galactic speed, which suggests another trivia question, one I haven't actually investigated. Although the Voyagers (and Pioneers, and New Horizons) are on solar system escape trajectories, they do not have enough velocity to escape the galaxy. But suppose one encounters another star many thousands of years from now. Could it provide enough of a gravity assist to eject it from the galaxy? How big a star and how close would the approach have to be? Assume the star is moving along with Sol in the same direction around the galactic center at 200 km/s.