Mr.Campbell ,
By the sunset fix you can see that Noonan precompted for checking position by celnav which was normal operating practice. For sunrise , due the on first leg delay , Noonan had to recompute en route since sunrise o/b would originally have occurred at the Turn Off Point before going inbound for Howland. If having gone astray , Itasca would have been long before 1912 GMT be warned by radio , but on the contrary : before 1912 GMT there was not any sign of distress. That holds Noonan precisely knowing where he was when commencing the approach procedure. Do we have any indication about this statement in terms of air navigation ? Yes we have : without exact initial calibration of latitude , the sunrise point of time having been precomputed , we know that the precise LHA of sun was 90-03-50 , computed by H.O.208 , Tab. II by navigator himself. @ 175453 GMT sunrise time the GHA of sun was [(175453) x 15] - 180 deg = 88-43-15. Thence, @ observed sunrise the longitude was : 88-43-15-W + 90-03-50-W = 178-47-05-W. The latitude was already contained in the precomputation by homework. Whatever pre-sunrise track was flown , great circle , rhumb line , any other initial point , From sunrise Noonan knew exactly where he was , given some decline from observation error. I do btw not comment for "make point" , if a computation is good you can safely follow I.Newton : Non fingo hypothesis.