The points you make are definitely logical thoughts (which can be rare on rf); however, it seems though that your assertion is not taking something into consideration that is central to christianity. You stated:
There is a, to the best of my knowledge, christian assertion that Because God's existence may be outside of the universe, that science can not ever verify his non-existence or existence, as science is limited to the observable universe.
This assertion relies upon the scientific observation that an object separated from a system, can not be accessed from within the system. It is true, and thus christians are correctly using scientific arguments to further their cause.
But, this same assertion ignores the obvious result of that same scientific principle. If an object is outside of a system, then not only can it not be accessed by something inside the system, but it can not access anything inside the system as well.
The laws that govern science are limited to strictly dealing with natural phenomena; therefore, testing of something supernatural (which christians believe) would be void. Correct? Plus, this is also supposing another system is governed by the same laws as this system, which would be impossible to conclude unless another system is scientifically found.
a. The observation, identification, description, experimental investigation, and theoretical explanation of phenomena.
b. Such activities restricted to a class of natural phenomena.
c. Such activities applied to an object of inquiry or study.