I have a bit of info on this topic, perhaps this will help:
William entered Cromwell's army after he was expelled from Oxford University under "the decree of unifomity, which required all students of the university to subscribe of all the articles of the Westminister creed." After the restoration of Charles II, he changed his name to Jayne (he was formerly DeJeanne) and secured a passage to America. He landed in New Haven, Connecticut, remaining there until after his marriage. He then joined a party of ten others, crossed the sound to Long Island, where they purchased form the Nassau Indians the tract of land on which the town of Brookhaven now stands. He was one of the origianl trustees of the villiage, serving unitl 1709, when he was succeeded by his eldest son William.
This doesn't have much to do with Cromwell himself, and for that I'm sorry, but I'll be on the lookout. Best of luck, Molly