Issues about captains, ships, and who they served

There seem to be some inconsistencies about which captain and ship served which Directors. On page 94 of Vol.V of Schetsen uit de Geschiedenis van ons Zeewezen, Jacob Duym is said to have served the Edam Directors and commanded the Zon (Vergulde Zon), but in Hendrik de Raedt's pamphlet and in Aitzema (page 822, Vol.III of Saken van Staet in Oorlogh in ende omtrent de Vereenigte Nederlanden) he is said to have been in the service of the Enkhuizen Directors. In the same reference in Aitzema, Hendrick Pieterszoon is said to have commanded a ship, the Man van Edam, an Edam Directors' ship. The Man van Edam must refer to the Maan, or Halve Maan, which was captured by the English at the Battle of the Gabbard. Again, Dr. Elias, in Schetsen, writes that Hendrick Pieterszoon was in the service of the Monnikendam Directors. I found the page in Aitzema because Dr. Ballhausen referred to it, in reference to his list for the Battle of the Gabbard, where he mentioned the Man van Edam, commanded by Hendrick Pieterszoon.