Hold it right there.
I just checked Rolls-Royce's web page (www.rolls-royce.com) and they said that the Trent 800 (rated between 94,000 to 104,000 lb. thrust) is aimed specifically at all versions of the 777-including what was originally called the 777-200X/300X versions.
Because the Trent 800 has been run at 104,000 lb. thrust already, all they need are a few improvements and the Trent 800 could be uprated to 115,000 thrust or more, which will match the GE GE90-1xx versions now planned for the 777 Long Range models.
This is why I expect Boeing and Rolls-Royce to make an announcement at least before the end of 2000 that the uprated Trent 800 rated at 110,000 to 115,000 lb. thrust will become the second engine choice for the 777 LR models.
Besides, the economics of the 777 LR models are obvious: the 777-300 LR has carrying capacity almost identical to the 747 "Classics" but has almost the range of the 747-400 and way, way lower fuel burn per passenger mile.