Here's the fundamental problem as I see it having played out so many times in "debates" between fundamentalist/evangelical* Christians and skeptics/atheists. The skeptic wants to see some kind of evidence or reliable reasoning from the Christian and the Christian keeps trying to push the discussion to the point where the skeptic concedes the possibility for a supernatural entity to exist. Once that point has been reached, the Christian then immediately asserts that that means that his own ideas of "God" and of his doctrine are true. IOW, if you concede that some vague undefined god-ish thingee might possibly have to exist, then all my highly detailed and extremely specific theology has been proven.
If I had a copy, I would at this point post that classic cartoon of two scientists/mathematicians standing at a blackboard. The one has worked out a solution to a problem and is presenting it to his colleague for comment. On the blackboard we see equations on the left and right sides, but the center is blank save for the words, "Something happens". The colleague points to that middle section and says, "I think this part needs more work."
Believers instinctively grasp at any straw that might suggest the existence of the supernatural as proof that their god exists and that the entirety of their highly detailed and extremely specific theology must be true. Non-believers, especially agnostics (ie, those who realize that we cannot possibly know anything about the supernatural which we cannot sense, observe, nor determine anything about including whether it even exists, let alone create highly detailed and extremely specific descriptions about it), know full well that you are jumping to conclusions (analogous in magnitude to leaping from the US west coast to the US east coast in a single bound) and so challenge your actions which put Superman Classic to shame ("Faster than a speeding bullet! More powerful than a locomotive! Able to leap over tall buildings in a single bound!").
IOW, that middle section that you overleap without giving it a single thought needs a lot more work. Just because there might be a chance that the supernatural might possibly exist does not in any way prove your own particular god nor any of the many theologies associated with that god. That case still needs to be made and as far as we can see nobody has ever attempted to even begin to make that case.
Personally I think you make a very good point and you put it well. I would point out that even at that you missed a step. The argument for an intelligent creator only gets you so far. After that you have to make the point for a theistic intelligence as opposed to a deistic one, and only then can you argue for your own understanding of of the nature of the god that you feel led to.
He has told you, O man, what is good ; And what does the LORD require of you But to do justice, to love kindness, And to walk humbly with your God.