I think Buddhism has a very nice take on the topic. It argues that the mind isn't actually a thing, but a process. So it's less of an apple, but more of a flame. So you can't really have half a process.

I think that you mistake the non-existence of something for the existence of something. I'll explain in an example:

A cat has one tail more than no cat (by no cat, I mean the non-existence of a cat, an empty place).
A dog is no cat.
Therefore, a cat has one tail more than a dog (no cat).
A dog has one tail, so a cat has two tails.

By using the non-existence of something as something (an object), you're creating a fallacy. Howether, the rest of the argument is very interesting, I never thought about the omni descriptions of god as elements that can be attributed to the universe itself. But I don't think all of the divine attributes apply, for instance, the omniscience would imply an awareness of things, and at least so far, there's no evidence for this awareness.