The sun rose at 1745 Z in the vicinity of Howland island. The sun climbed to six degrees at 1810 Z. The sun's azimuth changed to 066° at 1847 Z which would change the LOP to 156° - 336° so we know that Noonan did his calculations for the period prior to 1847 Z leaving about a half hour for the observations.
The NW intercept does make a lot of sense if that was the original plan. Perhaps the detour after leaving Lae threw a wrench in to those plans. I believe that cost them roughly about an hour and a half to bypass the storm.
Looking at the timeline for approach, when she stated that they were 200NM out at 17:42GMT, and they thought they had arrived at Howland at 19:12GMT, the speed of approach would have been roughly 150MPH. If they were already on the line, headed South taking readings, the should have already been on the line at 200NM out.
If you believe that they saw the Ontario at 10:30GMT and they were already on the line at 17:42GMT ("200 miles out") the ground speed achieved would have been about 153 knots versus 130 knots if they came straight in. Assuming a 23 knot headwind as reported by AE from the ENE, this would put their air speed at roughly 170 knots or 196 MPH. This speed would have required maximum fuel consumption. Of course if you do not believe that the Ontario was seen there is a possibility that the numbers would work out differently.
Perhaps FN had some other motivation for using the 157/337 line as an advanced line of position? He probably spent a considerable amount of time poring over the details of the flight before he left Lae. Other than seen Baker on the way, is there any other advantage to being on that heading regardless of your ETA?
Unless they were already on the line as you suggested, it does not make a lot of sense to stick to the line an hour later. They must have been following a magnetic heading at 20:13GMT. If FN was such a capable guy, why would they have not taken more readings after 19:12GMT that would have put them on a different heading? To me this would almost suggest that further readings were not possible due to the sky conditions.
The one advantage perhaps of stating that you were on the line was that they would know where to start looking for you had you told them that you were North or South of Howland. Because they did not include this information it was a toss up as to whether you looked toward the North or South. They chose North and did not find them.