I think something short like around 2 hours is a good distance to learn the plane, I'd go for maybe one of the Japanese regional flights that the 777 flies. 

 

 

From what I see from various airlines is custom ETP (coordinates) which are calculated by dispatch on the ground and entered into the Fix page.

 

That's the impression that I'm getting from what I'm reading as well.  The reference I'm reading says that ETPs are dispatch-only functions.

 

The related FMC display of diversionary information would be the alternates page.

 

Just my understanding...