Another way of looking at what you're talking about:
When we look at the world around us, is there anything that suggests that a God must exist? IOW, is there anything that we can find that's incompatible with the idea of a godless universe? If not, then why believe?
When I read your OP, the message I get from it is something like "we have theologically sound reasons for why our God is indistinguishable in every way from a God that doesn't exist at all." That's all fine and good to an extent - you dodged a bullet that could have proven your belief system wrong - you're still left with the problem that the God you're proposing is indistinguishable in every way from a God that doesn't exist at all.
IOW, you've left no intellectually honest path to accepting your belief system.
Now... if there can be no intellectually honest path to accept your belief system, this doesn't somehow exempt you from needing one.
Good points. I believe, the result of this discussion should also provide an answer, to your point that, is there even anything that suggests there is a God.
The point is, even if there are proofs of God, that proof and evidence would not be miracle. Because If there is an omnipotent God, then He must be able to show a Miraculous Sign, that immediately convinces everyone without a shadow of doubt, but then that means no one has the choice to reject. It will take away mankind's free will to believe or disbelieve. Thus, if there is an omnipotent God, who wants to provide evidence of Himself, He would do that in a way that, only and only if one searches for Him, then he can be guided to His way. This way, the free will is not taken from those who do not want to believe, while the way of recognition is available for those who willingly search after God.
So far OK?
Therefore there is no way, that anyone can convince or proof to someone else there is a God.
In my view, the majority of people who believe in God or gods, they do so for the wrong reason. It is often a cultural thing. It is often, due to the place and culture people are brought up, so, They just follow the common belief of the family and town or church.
But then sometime later in life, some of them realize their belief in a God was illogical and their religion was false, so they loose their Faith. But the majority who believe in a God, is only due to brainwashing from their childhood.
It could be even wishful thinking, that a God is there so they may pray to him and he answers their prayers and help them in their difficulties or fulfills their wishes in this life, and takes them to heaven in the next one. They become so dependent on this, that, no matter what, they will not be willing to give away their belief in a God.