The pilot in command is in the best position to assess all relevant factors and determine the best course of action.
I suggest much of that decision will depend on what training has been given to commanders.
Checklist land at nearest suitable airfield
There has always been the debate about land at nearest and/or ASAP.
180 minutes is strictly for dispatch in my view. If you lose an engine in an ETOPS twin you are still required to proceed to the nearest suitable airport in point of time for landing under FAA rules. And often that airport is not one of your designated ETOPS alternates.
There are times on overwater flights where the nearest suitable is also a 2-3hr ETOPS Alt'n. I don't know all the current twins so I wonder at the difference between MTOW & MLW? Suppose you are 3hrs out from departure; and then entering a 2.30hr circle to an ETOPS Alt'n and a problem occurs: You divert one engine out to the ETOPS Alt'n (huge commercial pressure to return, I know); you arrive at Alt'n >MLW. Surely no-one is going to dump fuel to delay the landing? If not then, they why anytime? I just propose the question for discussion, and also wonder what flight time is required to take the very large twins from MTOW to MLW.