The episode was “Visionary”, from DS9’s third season.
Brad Bird - MI:4 didn’t blow me away, but it was entertaining and showed that he could handle a big live-action movie. He handled character development better in his animated movies.
David Twohy - has a decent writing-and-directing resume, including action and sci-fi flicks like Pitch Black, The Arrival, and A Pefect Getaway.
James McTeigue - I think he did a great job with V for Vendetta, and I liked The Raven, too. He doesn’t appear to write, though.