IF I were you, I would download their electronic timetable. It really doesn't take long, about ten minutes at the most, and you instantly have ALL of their scheduled flights ALL around the world, with seat maps yadda yadda, meal assignments, and updatable monthly.
We have a few 777 out of DFW a day, Most to Asia, though some to Europe, and maybe... no, I don't think we have a 777 to South America yet... But I don't know the times off the top of my head.
When you get their timetable, you can click one of the buttons to view like an airport's entire schedule, and then sort it my aircraft... I do it all the time.