The date of H the 8 to E the 1 (around 1600) suggests a Spanish enemy; that is the period of the armada. The versions of the song that refer to a Turkish enemy may be later, when England's enemy was the Turkish empire, including the Barbary pirates in north Africa. The Lowland Sea is specifically off the Netherlands (Nether means "Low").
    I have read that in the late 1700's the Turkish galleys would catch an English ship becalmed and get on its quarter where it cannot bring a cannon to bear and pound it all day with a bow gun. A galley is moved by oars, usually by slaves, rather than by sails. A ship in this position is in a dire strait and facing a slow death; there would be time for a boy to swim the distance and drill holes, and the desparation to try anything. Also, the galley would not be moving.
    The usual counter was for the ship to launch a boat and pull or push the bow around so that its broadside would bear on the galley. The galley would try to sink the boat, and if they succeeded, the ship was back in the frying pan.
    In any era, as long as there are cannon so that the galley can stand off, a galley has this advantage over a ship when the wind is calm.
    This doesn't address the basic question of whether it is possible to drill a hole or if the hole can let in enough water; but it has been my concept of how the battle took place.