I operate ETOPS/EDTO a couple of times per month, so I have a genuine interest in this topic.
Once upon a time, twin engine high capacity turbine aircraft had to be operated within 60 minutes of an adequate airport.
In case one engine failed, the reliability of the remaining engine was seen to be no more than 60 minutes, based on statistics and the probability of a further in- flight shutdown. (My interpretation and understanding.)
That was as far as the authorities allowed us to go.
Even today, if we depart an airport that is closed for arrivals, we still need to provide a take-off alternate within 60 minutes flight time of departure at single engine cruise speed in case we have an engine failure during the departure. Why is this?
Safety of aircraft, safety of the passengers, further technical difficulties etc.
Then, we wanted to go further, so straighter tracks were planned taking us greater than 60 minutes from an adequate airport, and ETOPS/EDTO evolved.
Still based on statistics for an in flight- shutdown, 90, 120, 150, 180, 240 minutes from an adequate airport was granted, based on the regulators approval for such operations.
Often during ETOPS/EDTO, there are other available adequate airports closer than the ETOPS pair that can be considered. That is why my ETP pair is always the 2 closest available airports, in case something unforeseen should happen. ETOPS/EDTO just defines the area of operation. It doesn't dictate where you must go within the area of operation.
So, PKMJ to PHNL. It's great circle distance is 1981 NM. No other airports available. An offset ETP will be at slightly greater or much greater than half great circle distance (990 NM). It really doesn't matter as long as we don't fly more than 3 hours in either direction. Otherwise, we are flying contrary to our aviation authorities ETOPS/EDTO regulations. Refer CAO 82.0 appendices 4 and 5, EDTO.
United Airlines fly to Majuro 3 days a week in a B737-800, so the airport is more than capable of handling an A330. RNAV approach both runways. As good as an ILS. Would we have any qualms about performing the 34 RNAV approach at YMML? Probably not I'm guessing. Given 2 hours notice, how unlikely would it be that the airport, stipulated for such eventualities, would not be available for us to use? Forget PAX comfort for the minute. We are up to 3 hours over water from the closest available airport, now on 1 engine. Passenger and aircraft safety are the only things that matter.
At what point do we say continue to Honolulu. 3 hours before Honolulu? definitely. At 3.5 hours before Honolulu? most likely. Any longer than 3.5 hours when an adequate airport, let's assume with ok WX is available, at less flying time? Where do we draw the line?
It would depend on the nature of the problem, where the problem occurred, whether you continued toward destination while trying to sort it out, (should you turn towards the closest airport while trying to sort it out?), the possibility of further problems and where all this left you reference to either airport once the final decision was made.
Either way, the flight time remaining needs to be less than 3 hours on single engine.
It is all about passenger and aircraft safety within the regulations. Operator convenience and PAX comfort have nothing to do with it.