Apognophos,
What you describe is commonly referred to as 'last thursdayism' and is utterly unfalsifiable and meaningless.
if the creator is using any part of himself to produce the universe, then the complexity is the same -- whether he uses his brain or a portion of his body to construct the universe. The amount of information that he would be dedicating to the universe would be the same whether it came from what we would consider to be its mind or its body (its "active force", to borrow a JWism). It seems that most people assume that a creator would build the universe with new material that it summoned into existence, but this ought to be impossible. It's more logical to imagine that it must use a part of itself.
You are then stuck back with the same problem, this (god's spare third testicle) universe that you are talking about has the same level of complexity as my materialistic natural universe. You still have the same problem I described before, that the rest of your god (sans third testical) also has a seperate level of complexity.