The evidence is that Amelia Earhart ("AE") and Noonan landed, survived and radioed for help, the radio calls being received and DF'ed to the vicinity of Gardner Island (where they were). Fly over of the island reported evidence of recent habitation of an island that had not been inhabited since 1892--and this was 1937. No one actually went to the island to look. They caught fish, survived for a while, and probably perished from lack of water. They had enough equipment with them to survive. What they lacked was water.

AE's radio navigation skills were poor, and probably, along with possible damage to the antenna done during the last take off, got her into this position. They survived. But no one bothered to follow up on the evidence that was there.

22 years of research and several on-site expeditions by TIGHAR.org have pretty much reconstructed what happened. A good quick summary of their research is here:
http://tighar.org/Projects/Earhart/AEdescr2.html

So what they needed, as did Tom Hanks' character in Castaway, was a solar powered satellite phone. Not available to AE of course, but certainly available now.

So my addition to the S.S. Minnow is a solar powered satellite telephone.