Because the man described laws of logic appear to be inconsistent in some cases or incomplete in others(or rather in their aplication to mathematics at times) certainly doesn't imply that the universal laws are similar.
In this case, I think it does. Though I'm obviously no mathematician, Godel's proof seems to me to imply that axiomatic systems are not incomplete because they're weak or incapable - they're incomplete as a result of being strong enough to model number theory. That is, axiomatic systems don't become incomplete
until they've reached a sufficient level of power and complexity.
Now obviously the universe's logic cannot be weaker than our logic. Therefore we know that the universe's logic must be incomplete as well, not because it is weak, but because it is strong.
Now, how could your perfect god radiate such imperfect logic? Now, you may think that god's logic is not incomplete, but if it isn't, it can't model number theory. That's pretty weak, don't you think? Why would god have weaker logic than we do?