"My definitions and premises say nothing about the possible existence of a god or of an intelligent extraterrestrial much less the location of either's existence.
Personally, as you may know, I don't believe that gods exist but my argument here is neutral toward that proposition."
But your premises are supposed to be derived as an attack on a Christian argument. Premise 3 is undeniably so:
"According to Christian theology, all things in the universe were designed by God"
How is it that you have presumed to cite the contents of a Christian theological argument about 'things', 'the universe', 'design,' and 'God,' etcm while using definitions for those words that Christians would not use?
As it is, your definition of 'universe' was "all that is real," and naturally, by that definition, then, God cannot be real, because according to Christian theology, God is a real 'thing' outside the universe, but your definition of universe excludes- by definition- the possibility that God could even conceivably exist.
So, it seems to me that your argument isn't very powerful, even if granted. You seem to be going after the notion that the Christian God could be identified as the designer of the universe, but your definitions exclude it being possible for there to be ANY God outside the universe in the first place.
It seems to me that for your argument to have any force, at the very least you ought to be using the definitions that Christians would use.