A question that I am not sure how to even ask...

The DC said
Is it possible for sludge to be so thick as to do this or am I missing the obvious?

On a 51 year old engine?!? Yes. You're going to have to pull the valve cover and see what's going on.

The DC said
What is the solution regarding heavy sludge, if so?

There is currently another thread active about a sludged up motor and different opinions and ideas of how to clean it out. I would try to find that thread. Lots of good ideas. Good luck!