Frankly, I find metaphysics extremely difficult to understand, so I can't do much to critique the content of such an argument. What we can say to such ones, though, is that logical validity, while a necessary condition for truth, is not on its own sufficient; there must also be empirical validity.
Consider Zeno's paradox. You want to go sit on the couch, okay? So you start heading to the couch, but before you get all the way to the couch, you've got to first get halfway there, and before you get halfway there, you've got to get half of halfway there, and so on before that, ad infinitum. You're so busy trying to get infinitely half the distance to the couch that it is logically impossible for you to ever conclude you journey; you will never reach the couch! Fortunately for you, reality proves that you can indeed reach the couch, as evidenced by your currently sitting comfortably on it. So while it can be logically "proven" that you can never get to the couch, the logic doesn't actually tell us the truth about reality. The same would go for any logically sound metaphysical "proof" of God; without empirical proof alongside it, sound logic is just self-consistent ideas that don't necessarily translate into reality.