Irvine,
Personally I am walking through the flight plans and navigation issues so that I have a good understanding the challenges they face and understanding the history of navigation in that era. It is as much as a history lesson than anything else. While this thread is indeed speculation, it is just as valid as any other speculation (like the MC simulation as you mentioned). Anything beyond what is captured in photos, paper, and even witness recollection is speculation just as is the Niku Hypothesis itself. I am not troubled by the speculation as we are not spending 100s of thousands of dollars searching for the Electra and instead we are simply posting on an Internet forum kicking around ideas, the only expense is our time. It is a hobby and I do not think we should be very serious about this hobby.
Back to the conversation, you do bring up a good point about the 19:12GMT message. They certainly felt that this was the end of the line and that they should have been in the vicinity of Howland. What I am also curious about is what they did for the next 16 minutes until the 19:28GMT "we are circling" message. What happened in those 16 minutes could perhaps have sealed their fate. About a month or two ago Gary and I walked through the scenario of what they would do. Gary felt that they would have doubled back to where they were at 19:12GMT before they began the search on the 157/337 line. So they would have only traveled an additional 8 minutes then they would have to double back for 8 more. What is interesting to consider is the possibility that perhaps they did not do this.
If you try to put yourself in their shoes, looking out the window, hoping (beyond hope in this case) that the island was just about to pop in to your vision, just another mile or two, maybe to the left or right as you busily scan the horizon for even the slightest sign of something that looks out of place, knowing full well that your life is on the line, would you have stuck with procedure and started a stop watch so that if you did not find the island you could double back? What if after 16 minutes, they just said Ok, we should have seen it and then started circling at that point until they came up with a plan? I think that it is very plausible that reality set in and they might have began to panic knowing full well that they were out of visual range and had no idea where to look, long or short, in any direction. This of course all depends on the confidence they had in their ability to get a fix and to track their speed and heading. If you had a high confidence, you would more than likely double back as Gary suggested. What if you had no confidence? Why bother back tracking say 40 miles if you did not know if you were short or long that 40 miles?
What is interesting is that if they did not double back but were accurately tracking their heading and speed, just missing Howland by say as little as 15 to 20 miles, this would have put them out of visual range when they started traveling "the line" 157/337 which must have been an advanced line of position since they were not able to determine where the line was until at least 30 minutes after sunrise as Gary had pointed out previously. If I understood Gary correctly, they would not have been on this heading (North and South) had they been able to take a new fix using the Sun as by the time they did so, they would have used a different heading an hour later. This seems to suggest that they were not able to get a new fix after their arrival probably due to the conditions while searching at 1,000ft, probably below the cloud layer (although I have not seen an analysis of the cloud height around Howland that morning and this is pure speculation).
So while Gary is probably right that doubling back after the 19:12GMT message is the right thing to do, perhaps that is not what they did. That would explain why they did not find Howland at least on their first pass "on the line" searching for Howland and perhaps subsequent passes until they either searched and wandered out of radio range or as many suggest, or flew to Niku. I have not really formed an opinion yet as to what I believe as I see a case for both the splashed and sank theories as well as the Niku theory. I do believe they had enough fuel to get to Niku but I have not yet determined in my own mind whether or not this makes sense. I would guess that FN was well aware of Niku but also the rest of the Islands in the group. For myself, the most logical thing to do in my mind would be to head toward the center of the cluster of islands that formed at least a 130 mile wide target (if not more adding in the visibility range on either side of the cluster). Like most things surrounding the disappearance not all of the actions taken by AE and FN make logical sense like making such an attempt without verifying the radio (no belly antenna implied).