I think, respectfully, that you are making this much harder than it needs to be. Satanists(by which I refer to "LaVeyan" Satanists as that is my definition of such) are people who loath the idea of taking a title in the first place. Once they read the Satanic Bible and see themselves reflected on those pages, they accept the title of Satanist. It is really that simple. Satanism is a broad term that is meant as a frame for the picture that is you. It is a personal definition of who and what you are. It is the only title needed. There are multiple beliefs and philosophies that share common ground with Satanism but they are not Satanism.
On another note, concerning Peter Gilmore's introduction to the Satanic Bible, Atheism is in fact one of the other ideas that shares common ground. It is not just a denial of any outside force controlling the universe, but more importantly, it is a "faith" that embraces science and reason as "god". That is a Satanic concept but still, Atheism is not Satanism.
So many people try to determine what Satanism is through applying other titles to an already named philosophy. Satanism is unique and different from all these other ideas even though it may share similarities. If you spend all this time searching for other titles for yourself then you are not being very Satanic, are you?
"Say unto thine own heart, "I am mine own redeemer.""
-Anton Szandor LaVey, The Satanic Bible