There was no possibility of diversion. That's why she didn't divert.
She'd massively blown her fuel reserve quite early in the flight, even before whatever nav bust(s) occurred.
We have very little actual track data and most of that is a bit flaky, but let's look at the numbers.
Depart 00:00z from Lae. We know the position of the end of the runway, thanks to Google Earth, to be 6° 44.3'N 147° 00.0'E. Noonan would have used the published co-ords of Lae which were 6° 45'N 147° 01'E.
At 04:18z she said she was at 7,000' and declared a speed of 140, but didn't give a position. It's unclear whether 140 was in mph or in knots and even less clear whether it referred to IAS or TAS or G/S. We can only conjecture with that data, but any such conjecture is unfruitful. The altitude is presumably to stay above the weather, but it blows any chance of adhering to the economical fuel plan which required staying down at 2,000' feet for the first 9 hours and only climbing to 8,000' after 17 hours of flight.
At 05:19z she gives an altitude of 10,000' and a position of 7° 3'N 150° 7'E. The altitude is credible, though surprising. The position is clearly bollocks. If you want to mallet a square peg into a round hole you can substitute any Lat or Long (or both) into any theorised position for that time, but the more intellectually honest thing to do would be to set the false data to one side and move on. Her altitude of 10,000' shows that she'd massively blown her fuel budget in the very heavy climb. She shouldn't have been above 2,000' on the fuel plan at this point and shouldn't have been as high as 8,000' until about 18:00z. 10,000' was clearly necessary to remain VMC on top, but she paid a huge price in fuel to get that high so early in the flight.
Her position report of 07:18z at 8,000' at 4° 33'S 159 07'E is the only one of the entire flight which we can in any way corroborate. It is entirely consistent with the known nav plan and it is almost certainly based on a sunset shot. My own calculation produces a sunset time of 07:19:27z would have been observable on Noonan's bubble sextant at that place and aircraft altitude. This raises an interesting question as to whether Noonan's chronometer was correct. We know that he'd been unable to get a radio time signal at Lae to check the index and rate of his chronometers.
Her zero wind estimate for the flight was 18 hours. Her departure message gave an ETA of 19:00 which was based on the forecast headwinds in the first and second halves of the flight.
At 17:45 she declared her belief that she was approximately 200 miles from Howland.
At 18:15 it was 100 miles to go.
At 19:12 she believed that she should be "on top" of Howland. She declares low fuel state and estimates only half an hour left. That is presumably at cruise power and we can presume that she then pulled the power back to max endurance and quite probably had Noonan scavenging the last dregs of fuel from the emptied tanks.
At 20:13 she makes what was to be her final call. She says that they are still running "North and South" along the 155/337 LOP.
No diversion. No fuel to attempt one either.