If I remember my celestial navigation right, a sun line will only give you one line. You can be anywhere on that line. I those days it was 90% dead reckoning and 10% luck. If the winds were off and he was a degree or two off on heading....
I recall once during the SEA era hearing about a tanker navigator who missed Guam by 400 miles. Luckily for them, the Guam people was able to get a directional fix off the HF and steered them back to Guam.
I may be the only member of SOH (but more likely just one of a few) who actually did navigate an airplane across the Pacific and Atlantic Oceans using only celestial and pressure line of position techniques.
You are correct. A sun line of position (LOP) merely gives you a line (in actual fact a small segment of a circle) and you can be anywhere along that line. When flying from west to east, as she was doing, the sun line plots along the distance line, meaning more or less perpendicular to your west to east course line.
Pressure line of position can provide a course line, meaning a LOP that runs parallel to your west to east courseline.
I would believe that her navigator would have use the temperature method to plot his pressure lines. It is not all that accurate, but better than nothing.
The jet stream sometimes does come down in altitude and can radically and unpredictably alter the winds from their normal strength and direction, even at altitudes down to 5,000 feet MSL, or lower. It is suspected this happened on that fateful flight. Don't forget also that for celestial to work, you have to be able to see the celestial body you are shooting. Clouds can become a problem.
Back in that era, every cross oceanic flight was a risk, especialy the distance she flew on that leg, which was the longest scheduled leg of her around-the-world effort. So, being off by 300nm is plausible. Noonan's job was to get Earhardt close enough to receive the NDB signal that was supposed to guide her in. But it seems for whatever reason, the radio did not function. She was close enough to establish radio contact for some time, and in theory that meant she should have been close enough to receive and home in on the NDB signal.
But, clearly that did not happen.
Why has remained one of the oldest questions in aviation history.
Ken