Two nautical terms

Solution 1:

John Rogers, Origins of Sea Terms (1984) has this entry for "king spoke," which I take to be essentially the same entity as "king-pin" in Whitman's poem:

King Spoke (also King Peg) The spoke on a ship's wheel which, when upright, indicates that the rudder is amidships, or in line with the keel. It very likely was so called because it often was identified and decorated with a crown or other regal emblem, honoring the monarch. Nowadays it is marked by a simple ornament, perhaps a turkshead or a metal cap.

Normally, according to Rogers, to "heave" means to pull on a line (rope, cable, hawser, or the like):

Heave To pull on a line (e[arly] XVII [century;] p[robably] e[arlier])

But Whitman may not have felt constrained by standard nautical usage in this instance. In any event, it seems to me that Whitman is simply saying that the pilot has grasped the (normally) vertical spoke (or peg or pin) on the ship's (or boat's) wheel and then directed it it downward (clockwise or counterclockwise) to cause the vessel to change course.