Any idea what they used for a chronometer?
One minute of error puts you off about 15 miles.
Radio time checks? Photos do no not show a sextant port? It is unlikely they had a bubble sextant.
There was a hatch on the aircraft, so at 100 kts(?) out in the wind you make your sightings. Take three it will even it out!
Flying 6000 miles over open water and finding a very small island, wow.
Their most accurate nav aid would have been sunrise. With a good chronometer (not unusual at the time, esp for someone trained in maritime celestial navigation) position at sunrise would give them the longitude line of their position.
From there, using DR&P, they would have the longitude of their destination. Just have to determine the latitude (which they failed to do).
In previous “spats” over position with her navigator, AH would always make a right turn when she felt they were lost. If she did this on the last leg, it would point her toward Nikumaroro Island.