According to the following page, AE reported seeing a ship in sight at 10:30 GMT.
http://tighar.org/wiki/Nightfall_to_Ship_In_SightThis telegram seems to be the beginning of the assumption that it was the Myrtle Bank that AE might have seen at 10:30 GMT.
From: SYDNEY
Action: STATE
Precedence Datel 07/03/37 Referback KP0302XX (19370703101XKPH) Referforw
Classific Toffl 2200 Referback1 Referforw1
Style Referback2 Referforw2
Group 0 Datez 07/03/37 Referback3 Referforw3
Officeno SY Toffz 1200 Referback4 Referforw4
Text: PLAIN, SYDNEY N.S.W. VIA TUTUILA AND N.R. DATED JULY 3, 1937 RECEIVED 2:42 P.M.; SECRETARY OF STATE, WASHINGTON; JULY 3, 10
P.M.; AMALGAMATED WIRELESS STATE INFORMATION RECEIVED THAT REPORT FROM "NAURU" WAS SENT TO BOLINAS RADIO "AT 6.31, 6.43 AND 6.54
PM SYDNEY TIME TODAY ON 48.31 METERS, FAIRLY STRONG SIGNALS, SPEECH NOT INTELLIGIBLE, NO HUM OF PLANE IN BACKGROUND BUT VOICE
SIMILAR THAT EMITTED FROM PLANE IN FLIGHT LAST NIGHT BETWEEN 4.30 AND 9.30 P.M." MESSAGE FROM PLANE WHEN AT LEAST 60 MILES SOUTH
OF NAURU RECEIVED 8.30 P.M., SYDNEY TIME, JULY SECOND SAYING "A SHIP IN SIGHT AHEAD". SINCE IDIENTIFIED AS STEAMER MYRTLE BANK
WHICH ARRIVED NAURU DAYBREAK TODAY. REPORTED NO CONTACT BETWEEN ITASCA AND NAURU RADIO. CONTINUOUS WATCH BEING MAINTAINED BY
NAURU RADIO AND SUVA RADIO.; DOYLE
________________________
Dztzf 193707031200SYDNEY
Source: STATE Copyno: 0 Record No: 2358
---
The exact position of the Myrtle Bank seems to be up for debate, with two possible positions being estimated (Lexington Search Report, State Department telegram). Apparently TIGHAR has estimated a position of the Myrtle Bank at that time, roughly centered at 2°20′S, 167°10′E. The details are given here.
http://tighar.org/Projects/Earhart/Archives/Research/ResearchPapers/Worldflight/finalflight2.html---
There are several references to the position of the Ontario given as 2°59.02′S, 165°23.20′E, so I will accept that as being fact.
If we take the earlier calculations that I had done where the ground speed achieved from Lae to check point A and then on to check point B (Nukumanu Island) the ground speed achieved was approximately 124.5 mph. Just as an exercise assuming that she maintained this 124.5 mph speed from Nukumanu Island for some time going forward (say until the 10:30 GMT report) the time elapsed would be about 3.2 hours (10:30 - 07:18) after leaving Nukumanu Island. Calculating the distance, assuming 124.5 mph for 3.2 hours, this is about 398 miles from Nukumanu Island, at about the position 3°7'28.73"S 165°19'45.91"E, along the original flight plan. This would place the Ontario only 11.5 miles to the North East, well within spotting distance.
I am not quite sure why anyone would ascertain that the ship spotted would have been the Myrtle Bank since very little was known about her actual position. Irrespective of the possible scenario above, the Ontario would be a much better candidate for the ship being spotted since it was only 8 miles or so off the original planned flight path whereas the Mrytle Bank would be at least 26 miles away from the original flight path if we assuming the best case approximate position of the Myrtle Bank at 2°20′S, 167°10′E. The only reasoning that I can see for concluding the ship was the Myrtle Bank and not the Ontario was based on some prior speed calculations that were assumed to be fact. From what I can see, the actual evidence of the ground speeds achieved is pretty scant at best.
Using the same speed as above, if Dowdeswell on the Mrytle Bank had his time confused, and he really heard the Electra at 11:00 GMT (local time versus New Zealand time miscalculation?), this would have put the Electra within 30 miles of this coarse estimate of where the Mrytle Bank was estimated to be, nearly at the closest possible distance between the two. Since this report became important only after the fact, I can see how this time calculation could have easily been misinterpreted and / or documented incorrectly. Given that radio log errors and interpretations both at Lae and Howland are demonstrable, I do not think that this is much of a stretch.