The 767-400LR I can see as a plane that UA would want to look at closly.
First things first. There is no way that UA would send that to Hawaii. We have already replaced the DC-10s and the 747-200s to Hawaii, with 777s and 767s.
Now, what UA needs to begin looking at are the 767-200s. Some of those birds are getting up their in the years. Although, most will be here for another ten years, as the 762 is well maintained, it is quite, it is common with the 757, and it does its job cheaply and efficiently.
Now...why might the 764LR be good for United? Simple, now that UA is cutting capacity on teh 777s and the 763s, there is a large gap. A gap that could be filled by the 764. The 764 could be set up with about 215 seats to be the middle plane between the 763 and the 777.
Now, I think that if UA were to get this plane, that we would see two very different configuartions. One would be with an extended first and business class cabins, allowing for more capacity on the SFO/LAX-JFK routes. As well as on some routes that warrent the premium cabin space of a 777 or even a 747 but it would not be ecinomical to operate one of those larger planes on.
The second configuration could be with a more normal 767 seating arrangment. Each configuration would be ETOPS certified and have PTVs.
Routes that could be served by these planes are:
And so on.