Its funny that you mention John Donne's poem. I actually wrote a paper on his work in college. I don't see how the poem relates to a cowardly death like suicide.
"Death be not proud, though some have called thee" is a testimony of faith. The poems purpose is to declare victory, not defeat.
In every respect John Donne is saying that though we die, we can never die. He is saying that he is not afraid, that Death is nothing. It is a religious work.
These are not the thoughts of someone who would kill him self.
I only say this because it seems like you are interpreting the poem to mean that we should not, or do not, die proudly. this is a strange idea to me.
And I don't know know what else there is to hear. The man left a suicide note, that pretty much makes everything clear.
"And death shall be no more; death, thou shalt die."
