>The idea of "new doesn't affect old" is an idea based on logical and temporal consistency. God is not bound to those.

That entirely depends on your specific god belief. Suppose someone believes that god is the eternal principle of consistency?

>Well, let's instead start with the more common conception of God as limitless and with total arbitrary power.

If god is capable of anything can god decide to make it such that there is no god? Can god decide to self-limit god's own powers? If god intrinsically encompasses all possibilities does that include the possibility of godlessness?

You quickly get to then point where the concept ceases having any meaning.