Incidentally, if the writers are actually smart enough to use the Novikov self-consistency principle properly (which I'm not assuming, but let's just go with this for a minute), then that could provide an explanation for the various times when seemingly improbable events occurred because (according to various characters) it was "the Island's will", or some other mystical-sounding nonsense. For example, Michael tries to kill himself in "Meet Kevin Johnson", but the gun won't fire, and Tom tells him that he couldn't kill himself even if he wanted to. This would actually make perfect sense if there's a time traveler from the future manipulating events. The time traveler has evidence that Michael lived long enough to pose as Kevin Johnson on the freighter, so when he manipulates events in the past, he knows that, whatever happens, Michael can't die before serving on the freighter's crew.
Similarly, you could have Claire being saved by a time traveler before supposedly being "killed" by her house blowing up. The time traveler takes her into the future, giver her the downlow on what's going on, and sends her back to the present, where, rather than being a ghost, she's actually just someone who's now been given all the secrets about the island and time travel.
Not sure if all of that tracks. I'm just thinking out loud here.