How does Anatomy of Melancholy fit into the history of this genre of literature? Is there a name for it, and could you help point me to other...

This is a great question! The work itself is one I would characterize as a hybrid of philosophy and psychology. I think what you are finding appealing here is that it was written long before both philosophy and psychology became narrowly specialized academic disciplines and it tries to grapple with the big problems of how we are to live our lives in a holistic fashion. The book distills not just vast learning but also wisdom about human nature and emotions. From the other books you have listed, I think there are some other writers I could suggest for you. I also think that you might enjoy pursuing a degree in history of philosophy or religious studies -- most professors in those fields would be delighted to have you as a student.

The starting point for your reading should really be antiquity, as the writers you enjoy were saturated in classical culture. First, Aristotle's Nicomachean Ethics is the starting point for much subsequent ethical thought. Epicurus' Enchiridion is short and readable and is a good starting point for thinking about how one is responsible for one's own emotions. I suspect you would also enjoy the Meditations of Marcus Aurelius (another Stoic) and Boethius' Consolations of Philosophy (written as he was in prison, had been tortured, and was about to be executed). 

As you move towards the present, the works become more technical, and often take as a starting point the question of how we can know things or make ethical judgments. Some interesting ones for you (in roughly chronological order) might be:

• John Locke's An Essay Concerning Human Understanding underlies much of Enlightenment thought. 


• David Hume's An Enquiry Concerning Human Understanding takes Locke's skepticism even further; Hume really struggles with how we can have ethical beliefs in face of epistemological uncertainty.


• Edmund Burke is somewhat similar to the philosophers you enjoy. Two major books are: A Philosophical Enquiry into the Origin of Our Ideas of the Sublime and Beautiful and Reflections on the Revolution in France.
  
  


• Immanuel Kant is a towering figure in philosophical thought. His Groundwork of the Metaphysics of Morals is brilliant but difficult reading (he is extremely precise in language and thought -- but his writing is so dense that it may take an hour to get through five or ten pages, in my experience). He is especially important in the way he addresses the concept of moral duty.


• Matthew Arnold is quite similar to Emerson in being an essayist who addresses philosophical and artistic issues together. Culture and Anarchy and Hebraism and Hellenism are two essays of his you might enjoy. 


• Friedrich Wilhelm Nietzsche is also a fascinating author who has the same reflective breadth as the others you enjoy. Three of his major works are: Thus Spoke Zarathustra, Beyond Good and Evil, and On the Genealogy of Morality (1887)


• Bertrand Russell wrote many works of popular philosophy in a quite readable style.


• Richard Weaver is a deeply conservative and religious author who also is enormously erudite and deals with broad moral issues. Two of his most important works are: Ideas Have Consequences and Language is Sermonic.


• On a more liberal side, Nussbaum's The Fragility of Goodness also addresses the question of how to live a moral life.