God is so quiet

[Angrboda]

So God is, by definition, necessary (according to what you just argued).

Yes--because the definition of God literally contains the notion that he is not contingent. If you try to insert that he is contingent, you get an infinite regress--and therefore meaningless to insert that concept. 

As a matter of principle, God's necessity is an accidental property, not an essential one. God would still be identifiable as God if he were contingent, so necessity isn't essential to the definition of God. You may believe in a God who by your requirements is a necessary being, but that is you putting conditions upon your belief, not an indictment of the concept of a contingent god. In a way similar to Kant's example that a hundred imaginary thalars share the same properties as a hundred actually existing thalars, a God that is contingent shares all the same essential properties as a God whose existence is necessary. They are in essence the same.

As a response to the general question argued, no, a possible world where nothing exists is not logically possible because if nothing exists, then there is no "world" there. The universe is defined as everything that exists. You simply cannot have a "world" where neither God nor the universe exists, because that by definition is nothing, not a world. Duh. A possible world by definition is everything that exists; if you have no thing, you don't have a world. So, no, the universe doesn't fit your definition of what makes something contingent, even if I agreed with it, which I don't. (You are also unintentionally conflating imagine with conceive. You can imagine a situation where nothing exists. Whether you can conceive a situation in which nothing exists, using your definition of "logically possible" is a higher bar, and one you haven't demonstrated.)

ps. I'd like your input on the following post, HERE.