And Eru Smiled

[Son of Númenor]

2: Because of the corruption of some created beings, evil exists as (primarily) greed, pride, and fear (from which flow hate, etc.) and drives thoseof it to attempt to separate themselves and be independant of Eru. This constitutes a sort of spiritual suicide, since all existence is a part of Eru. (Iarwain)

I perfectly agree with this, particularly the part about evil's want to be independent of Eru and the emotions/'sins' that you pinpoint as the manifestations of evil. In some of these topics, threads seem to stray far into the abstract and philosophical, but your theory, and this part in particular, is very well-grounded in Tolkien's beliefs about his world, imho.

I do not understand, however, your suggestion that Melkor had "remnants of goodness" within him. It says in the Silm (which is conveniently packed away in my luggage in the car so that I cannot quote from it) that Melkor's evil is complete and utter, and that he has become so corrupt that any chance of his thinking a 'good' thought (much less doing a good deed) is beyond hope. This, actually, raises an interesting question: does exercising one's will in an 'evil' way, to become independent of Eru and attempt (as in the cases of Sauron, Melkor, Saruman) to become an omnipotent tyrant, in the end ultimately negate one's Eru-given 'free will'? Does this wilful act of rebellion put an end to the 'free will' so that, as in the case of Melkor, the rebel can no longer act out of goodness, and is utterly controlled by evil?