A few years ago BA did Brussels:Melbourne direct and it was at the time the longest commercial revenue flight, but not scheduled. It was carrying Blair (Uk Prime Minister at the time) and his whole entourage from an EU summit directly to the closing ceremony of the Commonwealth games.
From memory around 150 PAX, total trip time was just under 20 hours using a 777-200ER (297T MTOW) so a 777-200LR (which BA do not have) would go further (around 340/350T MTOW). It was a true revenue flight carrying a decent load for a real reason and not just a record attempt with negligible passengers onboard.