The TIGHR project has accumulated an amazing amount of data, but what I found with them has me fairly well convinced that their theory is wrong. I believe she had to ditch at sea somewhere near Howland Island, then floated for a few days until the airplane sank.
The most convincing pieces of data to me are radio based:
1) That she reported flying at 1000' under the clouds while searching for Howland.
2) That winds blowing from the east on a NW course would make it less likely for the course to have been south or east of the island.
3) That the weather reported at Howland was cloudy to the north and clear to the south
4) That she only had a 50W GE transmitter
5) That at a 1000' antenna height, the horizon is about 32 miles away.
6) That there was an increasing signal strength received by the USCG ship Itasca several hours before dawn culminating in a very strong signal in the hour before communications was lost
7) That Nikumaroro Island(Garner Island) is more than 400 miles away from Howland.
8) That the combination of distance, horizon, transmitter strength and signal strength make it very unlikely she was near Nikumaroro Island.
9) That the combination of transmitter strength and signal strength practically require that she was within 75 miles of Howland.
There are those who find solace in her landing on an island, surviving and fighting to survive. But the most likely result is that her plane is resting under thousands of feet of water to the NW of Howland Island where prevailing currents would have caused it to drift.