I took the 8:40am IAD-Den quite frequently and that one is (was last year) the 777. I usually cleared (1p part of the time then 1K rest of the time) and it seemed like there was usually some room in business class. Even as a 1K I frequently did not clear on the flight i took back from DEN-IAD - don't remember the aircraft, but it was not a 777, just a regular small 1st class section with 8 seats. It usually left DEN at ~6:30 and got into IAD around midnight.

I would think on the 777 IAD-Den you have a relatively decent chance (relatively being that it is hard across the board to clear as a 2p these days since there has been so much dilution).