The internet is incredible.
With the advice of someone else who also has a Westerbeke 71c-Four that emailed me, I was able to remove the coolant reservoir/exhaust manifold and move it to a bench where I could actually see what I was doing and clean the hole out.
He says that he has to clean that hole out every once in awhile so I guess this is a common problem with these engines. It will be on my regular maintenance schedule from now on.
Now I just have to clean the manifold up and repaint it before putting everything back together.
My thanks to the group.
(By the way, I took it by a radiator shop and their advice was not to worry about the scale on the inside - apparently, the photo makes it look worse than it actually is).
In the first image, you can see a jeweler's screwdriver being poked all the way through from the outside.