I think that you might need to broaden your frame of reference in this question. Your initial assertions are right in that the “captain” represents Lincoln and the citizens are “the swaying mass.” Yet, I think that from this point onwards, you need to widen the perspective and not seek to create a persona for each image. There might be more to it than this reduction. Whitman writes an elegy, or a mourning, for the President that he believes was the best leader in the young nation’s history. For Whitman, the promises and possibilities of America, are embodied in the hope and aspirations of Lincoln. With his death, an experience that Whitman believes is conveyed through the ideas of “cold” and “dead,” there is a loss of leadership on a profound level. This loss is something that is akin to a boat losing a captain. Whitman feels that the role Lincoln played in seeing the nation through a Civil War represented a treacherous journey and the war’s resolution is where a sense of safe has emerged. If you see the poem in this light, I think that the images become crisper and clearer in understanding both Lincoln’s role and Whitman’s analysis of it.