One thing that I have always thought interesting is that a sextant box was found on the island with that skeleton but no sextant was located. That seems a bit odd doesn't it? I mean, if it were just a box and the sextant was lost when the became a castaway, it seems that the person would either use it to hold items like food or water or it might as well be burned if it served no purpose. Even if this was some castaway and not Amelia, it makes no sense to salvage and hold on to an empty box and do nothing with it. Perhaps it did have a purpose but I have not heard any mention of it when the skeleton was found.
Another possibility is that it actually did hold a sextant and some other person walked away with it attempting to find their way back to civilization. Assuming that it was Noonan that could have walked away with it, and say attempted to build a makeshift raft, could the sextant have been used effectively to sail to a reachable destination assuming that he had no maps? Could you realistically survive a journey long with enough food and water to sail East until you hit land? I suppose you would be dead either way and you might as well go for it. The only probably I see with that theory is that he did not carve something in to a tree or arrange stones and sea shells to spell their initials out to let people know for certain that they did survived.
Another problem with the survivor theory is why not take a box design to hold your sextant?