How about taking these two problems as keys to open each other?
On one hand you say that for you the SoA philosophy seems as Abrahamic. On the other, you say that you cannot grasp how the most basic tenet can be the reversal of the role of Abrahamic God.
If these two are meditated intensely in the wide space of universal esotericism, the magical world view, it can happen that the lock opens, and from the seemingly Abrahamic puzzle box emerges something completely different, wearing quite a different face.
For neither is our Jesus the Christ of the Christians, nor our God the God of Jews, and our Satan is not the Satan of either. These are just the words to operate in the space where we lack other kind of deep enough cultural associative instruments to delve in the mystery of the Absolute, creation, and evil/suffering. In case SoA would operate in the culture which had no understanding of Abrahamic religions and their usual intuitive misunderstanding, the completely different terminology could have been adopted from the start. There would be no need to first introduct Christianity, Jewish faith or Islam to that culture to then build Azazelian philosophy upon such foundation. We could start straight away with talking about Shiva and Shakti, or the Taichitu, or whatever would be the instruments available at hand. The most important core of deconstructing the omnipotent patriarchal figure would adopt a different mask & different names, but the idea about joining the opposites in a certain way of ascension would still persist. The differences in forms would certainly have their effect on the whole outside of the brotherhood, but not its heart of being.