As you probably know, the Byams were a very prominent colonial family. William Byam, who was born on March 9, 1623, was Governor of Surinam. When the colony was ceded to the Dutch he moved to nearby Antigua, where he founded the line of the Byams of Antigua. My ancestral aunt, Amelia Jane Byam, was a member of this line. She married the Swedish-American inventor and naval engineer, John Ericsson. I have a copy of the royal genealogy of the Byams which I would be happy to mail to you directly if you like.
Best of luck,