Albemarle Sound can get nasty, but is usually OK in the early AM. When I run down the Chowan (live way up river), we usually stop the trip at the Edenton bridge as the water gets pretty angry around there.
A restriction downstream of the pump is only thing that causes hi pressure. Check the oil / PS cooler for blockage on inlet side. Was the old impeller 100% intact when it was removed?
A big problem with today's monster commercial ships is there are so few aboard the ship to station at every potential trouble spot.
As anyone that was in the Navy engineer type ratings aboard a larger ship can tell ya, when leaving / entering any port (called anchor duty) or underway...