This class could be a candidate for the refactoring exercise of "extract an object that you don't think is there"?
Perhaps, for example, you could extract a method object that would allow you to refactor several of the 50 line methods into members of an extracted class?
Alternatively, encapsulating some of those private methods that contain business logic in a new object that collaborates with this one might provide a new way to reuse either this object, or the extracted one.
One line is enough to consider refactoring. 40 each 50 line methods is starting to scream "I'm too complicated, there's another object hiding in here" to my ear.
