Earlier use of this argument for the necessity of evil? I seem to recall hearing or reading that Augustine posited that perhaps evil as such did not exist, i.e., that evil is more a void or absence of existence.  I think this line of reasoning is used to indicate that God did not create evil as such.

Is there a documented extension of this reasoning along the following lines: In order for God to cause to be an other that is not God (the term begetting would presumably be used for causing to be an other that is God), some absence or void would be necessary and that this void is constrained to include evil (whether because any conceivable void of this nature is "unGodly"/evil or because God's will to maximize the glory of God "compresses" such a void [i.e., one could conceive of a non-Godly but not evil void but maximizing the expression of "Godlikeness" constrains the void to be evil] or perhaps some other reason)?

(This line of reasoning occurred to me and I wondered if anyone had already considered it and thought it plausible and worth recording.  It seems a basic enough extension of a known argument that it probably came to someone's mind at some point, though it might have been rejected as absurd or useless or just not worth recording.)
You are right that the idea of evil as the absence of good is traditionally associated with Augustine. As far as I understand your specific idea, you are positing that 'absence of good' is necessary for anything that is not God, or that nothing aside from God can be wholly good.

This reminds me, more than anything else, of the Gnostic world-view, wherein all created beings emerge as "emanations" from the Godhead, and are more and more corrupted as they get further out from the source, like light from a candle in a dark room. In particular, the material world is inevitably impure (but can be transcended through spiritual discipline, perhaps thanks to some spark of goodness from above that is embedded in each human soul). There are many nuances within Gnostic traditions, and a lot of mystical / esoteric stuff, but this is the broad thrust.

In relation to Christianity, there is a fascinating history of conflict - though as usual, we almost always get the orthodox perspective, which may not be entirely fair to what actually happened. The problems early Christians encountered with Gnosticism include:


Inherent sinfulness of the world, perhaps created by Satan / the Demiurge versus God's love for the world - he created it, nurtures it, and considers it good.
Unimportance of moral behavior in the physical realm versus Obligation to behave correctly and do good works
God as pure inaccessible Spirit versus Christ incarnate as a man (living, suffering, dying)
Esoteric practice (levels of initiation into mystical secrets) versus Exoteric (proclaim the gospel to all)


Ultimately, the difference in Christology was the key marker of Gnosticism as heretical. The Gnostic version of Christianity held to docetism whereby the incarnation was an illusion, the true Christ being only spirit. This belief is contrary to certain passages in Scripture which we believe to have been explicitly written against Gnostics (e.g. 1 John 4:2), and it was definitively rejected at the first ecumenical councils.