Its clear that AE's belief that she must be near Howland could have been just as mistaken if she had encountered stronger than anticipated winds ( I know that she was too low for the jet stream).
There is a wind study somewhere on the site that proposes she ran into headwinds she did not know about, and probably ended up at least west of, and probably also south of, Howland, before following the LOP.
I believe AE was very close to Howland, probably just out of visual range. That could have been ten miles or less given the likely broken cloud cover at the time. This based on very strong signals on that transmission and also how late she was for the rendezvous. If she was that close, yet still west of Howland, the 157/337 line would have brought her within visual range of Gardner, yet just outside of visual range of McKean (which explains why they didn't end up on McKean).
There has been a major alternative theory in the forum about AE conducting a box search, after her last transmission, beginning with the LOP as the first leg of the box search. What is never addressed is the large amount of time that transpired between her expected arrival time and the transmission "we must be on you but cannot see you". It is probably a significantly longer amount of time than it would take due to headwinds. I believe she was probably conducting a box search during that time, not after her final transmission.
In her last transmission, her words are recorded in the log as "we are flying on the line north and south". If she actually said "we are flying on the line north
then south", it all makes sense. The two words would sound very similar, especially on her overmodulated radio. It would be their last attempt to find Howland. They probably didn't know for sure if they were north or south of Howland, so they would naturally follow the LOP first north, then, if Howland were not found, they would likely fly south along the LOP because they knew there were islands down there.
All conjecture, of course, but I believe that is precisely what happened.