One last comment, as to the question of perhaps Symon Oversee owning a ship. In the Virginia Colonial Records, "High Court of Admiralty Records "dated October 5, 1652, examinations taken at Plymouth..."Cornelius Symons, skipper of the Rotterdam: carried a cargo of mixed goods for the account of his two sons, one of whom, Symon Overzee, lived in Virginia, and headed for New Netherland. (...)." The issue was in regards to the Acts of Parlement prohibiting the Dutch and others from trading with Virginia and not allowing foreign ships from bringing goods into England which were not of their own country.
That as a side note, perhaps John Caine was a mate aboard one of Symons' ships.
Library of Virginia; Richmond, Virginia; High Court of Admiralty. Examinations on Commission; Author: Public Record Office Class HCA 13/253 Part I.; Description: List of High Court of Admiralty Records. HCA 1-32, p. 60; Survey Report: SR 11335; Film Number: Not Filmed. Ancestry.com.