I have been listing to them for years, maybe as far back as 2008, They seem to board ships from other countries and pilot them into Delaware river ports. I have seem some of there boats in the Philadelphia area but I don't know where they based. You can always hear them telling the ship captains to put over a rope ladder 6 meters above the water line for boarding.
The Maritime Exchange for the Delaware River and Bay, a not-for-profit trade association, is dedicated to promoting and encouraging commerce on the Delaware River and Bay. Our members, comprising all facets of international trade and related businesses throughout Pennsylvania, New Jersey...
Depending on your location - you can hear the Philadelphia Maritime Exchange office on Channel 14 156.700 or the Lewes Pilot Tower.
What you have been hearing is the Lewes Pilot Tower (a picture of it shows up first when you open the web site of the Maritime Exchange). They have a schedule of ship arrivals and departures through the Maritime Exchange and begin to communicate with inbound ships coming up the sea lanes to the bay entrance. The pilot boat is usually dispatched to place the pilot on the inbound ship around a buoy in the area between the Delaware Bay entrance and the Atlantic Ocean. This is one of the pictures I found with a google search. The Lewes pilot tower is located in Cape Henlopen State Park in Delaware.
The radio signal strength from the tower does change - I think they keep it on low power and then switch to high power when the ship has difficulty hearing them. So the times you are listening may have just been a high power time (if this is the first time you are hearing them).
I hear the tower routinely from my Villas NJ location and occasionally can hear the Philadelphia office as well. Here are the licenses as displayed from Radio Reference for Sussex County Delaware
The pilot tower usually identifies itself as WHW819 over the radio on channel 16 and channel 14 when talking to ships or even the USCG. Another interesting function that the tower performs is calling ships that are within the North Atlantic Right Whale Transit Zone. When the monitor a ship on AIS exceedng the 10 knot speed limit - they contact the ship and advise them to slow down and the reason why.
the area near the mouth of the bay is marked below (I circled it in blue)
I am on the Delaware right by the Burlington-Bristol Bridge and I regularly listen to channel 14, The Maritime Exchange. 24-hour Channel that seems to log and keep track of the large Ships coming and going on the Delaware
Ships Come regularly out past me to the port at USS Steel. If a captain is not qualified on the river then they are required to have a pilot. The name McAllister comes to mind and a lot of the tugs I see going up and down the Delaware through Bristol have the M on the smokestack.