No such close islands from Cat. Columbus reported Island II had a coast running North-South. No such coast at Conception. Even if there were such a coast, it would not face Island I, as reported by Columbus. Island II must be at least 5 leagues north to south.
Conception is much smaller.
Island II must be at least 10 leagues east to west. Conception is much smaller. Columbus reported distance from Island II to Island III as 8 or 9 leagues. Distance from Conception to Exuma is 15 leagues, or from Long Island is 5 leagues. Although there are many anchorages at Exuma, they are farther than this from either end of the island.