If you remember the theme song it was only a "three hour trip". A tourist boat can make about 12 knots so a trip of that sort would put them only 30+ nautical miles from Hawaii (their shove off point). No way there would be "an uninhibited island" within that short radius.I don't know if the writers of Gilligan's Island knew that, but that is how the castaways' AM radio was able to pick up stations on that distant island in the daytime.
I do remember my destroyer being able to receive KORL (AM) a full day before reaching Pearl Harbor (24 hours X 16 knots).
At any rate, when the Professor can make a radio out of two coconut shells and a jar of octopus fluid, the distance of an AM signal is not much of a long shot. 🙄