A picture or a good description would help... First though was a seagull, however crows can imitate noises... however by your description of it's wingspan you are indicating that this bird may be half the size of a crow?
Another idea was the booby [bird], who have webbed feet, a long beak.... but are still rather large birds mostly found near the shore... on that note however I have found a video of something like wind blowing over something... however I can't tell if its the birds or the people...
YouTube - Birds in Love
However, these videos confirms that it comes from the birds....
YouTube - The Masked Booby, Lone Ranger of the Galapagos, Ecuador
YouTube - Blue-footed boobies courting
YouTube - fighting blue footed boobies
The only thing is, is that I haven't found any other noises that they may make that fit what you were describing...
There are the shore birds, such as wandering tattlers, and whimbrel who are long legged and long beaked birds, however have short/stout bodies... but again they are shore birds....
I don't really know about the wildlife in Kwajalein, and only was able to figure out some of the birds that live there by doing a small bit of searching on Google...