It seems to me that the "200 mile" message couldn't have been from a dawn sighting; it was logged at Howland 3 minutes before the sun rose there. AE and FN's local dawn would have to be at least a few minutes later than Howland's.
The "100 mile" message might be after FN had done some chart work with the dawn LOP.
I think that the 200 mile report would indeed be based on Fred’s observation or anticipated observation of the dawn line time.
AE made the 200 mile out report at 1742-45z which according to the almanac tables was the sunrise time at Howland and was on her scheduled transmit time. Also, according to the tables, sunrise time at the coordinates for 200 miles southwest, bearing 258, was 1757z or 12-15 minutes after her report at 1745z.
Perhaps because it was twilight, Fred was estimating that the sunrise was 12 minutes away when he gave her the 200 mile note, therefore, they could have actually been about 227 miles from the Howland LOP. 12 minutes x 2.25mpm=27 miles. For the Electra to have covered the distance from the position that it appears to have been at 1745z, to the reported position at 1912z, the ground speed would be about 150 mph which seems a little fast. If their actual position at 1912z was still about 10-15 miles west, tracking inbound to the Howland LOP, then the ground speed would have been about 140 mph and seems feasible.
Fred was obviously a very competent navigator and understood the importance of an accurate time check. Their departure from Lae was delayed until he could get an accurate to the second time check that he knew he would need to use the almanac tables. This indicates that he planned on plotting the LOP at sunrise to determine how far they were from Howland.
I do not sense that he would have simply relied on radio navigation. His expertise was in celestial navigation. His intent was to find the island by the LOP method with or without radio navigation. If AE could get a directional bearing from the Itasca, then they could find Howland, nevertheless, he was going to use his sightings, charts and chronometer to the best of his ability. Doing so is what probably saved them from having to ditch in the ocean. Without a radio bearing to the Itasca, it was almost impossible to hit the island. With an elevation on the island of only 20 ft. and flying at 1000 ft, it would be impossible to distinguish it from the sea.