Let’s look at the second half of the original snippet.
True!—nervous—very, very dreadfully nervous I had been and am; but why will you say that I am mad?
The second quality is much more simple. It has no repetition, no describers and no intensifiers.
Why did Poe keep it simple in this instance?
What if Poe had written something like the next example?
Nervous — very, very, dreadfully nervous I had been and am; but I am not fearsomely, terribly mad.
If we add more qualities to the word mad:
By keeping it simple and by putting it right at the end of the sentence, Poe makes the word “mad” cut through, and helps emphasise the narrator’s denial.
Let’s write some variations on our simplified version. Have a character admit to one extreme state of mind, but reject another.
True! Nervous — very, very, dreadfully nervous I had been and am; but I am not mad.
Of course! Sad — so, so, deeply sad I had been and am, but I am not miserable.
Yes! Angry — very, very, violently angry I had been and am, but I am not murderous.