While I don't quite share some of your feelings on right and wrong (I believe that while much of what we label right and wrong is neutral, or rather in a gray area, there nonetheless does exist a threshold upon which passed is absolute right or absolute wrong), I'm not too far off from your general idea all things considered ("non-dogmatic theism"). At least not compared to most other ones.
I consider myself a Deist. I believe in a God, but I do not believe that God exists in a form remotely akin to what religion teaches. I believe we have fallen prey to our tendency to anthropomorphize everything around us in an attempt to better relate to it. The idea of God as an individual, as we consider an individual, just doesn't work for me. Einstein had a quote that played at the well known teleological "watchmaker" argument.
Quote
"I see a pattern, but my imagination cannot picture the maker of that pattern. I see a clock, but I cannot envision the clockmaker. The human mind is unable to conceive of the four dimensions, so how can it conceive of a God, before whom a thousand years and a thousand dimensions are as one?"
I like this quote very much. I believe that the teleological arguments are sound, as are some original mover arguments. (I cannot recall who it was, but I remember a story about two major philosophers debating during Enlightenment, I think using Aquinas's ideas as the basis for the argument. The atheist in the end conceded the validity of the argument, but said that it was irrelevant because it did not logically prove a specific God, in that case the Christian God.)
Going back to the watchmaker analogy and Einstein... If you find a watch on the ground one day, and begin to take it apart piece by piece, dismantling it to see how it works, you will be quick to realize that everything appears as though it were designed to work together. Each piece has a purpose, each purpose a piece. Now there are two options... 1) This watch was the product of pure chaos and randomness. Nothing within it could not exist within nature, and given an infinite amount of time those things would eventually fall together in a specific pattern that worked in this fashion. 2) A designer built it. Occam's razor says go with the hypothesis that has the least amount of assumptions. Well, there are a TON of assumptions in option 1, including about the nature of time. In option 2, there's only one assumption.
I look at the design of the world and I infer a designer. But that is where it ends. I look at causation and I see an original mover. But that is where it ends. I infer a God, but not a specific God. I also know that we humans are absurdly limited creatures in the scheme of things. Einstein is right, we can't even perceive 4 dimensions, when there are potentially infinite. We can't perceive the true nature of time, and we can't even perceive the true nature of our own physical reality (most of what you see at any given moment is extrapolation and not "real", simply assumptions your brain has made based on previous data). What chance do we have of conceiving God? Yet nonetheless, I believe God exists.
Ergo, Deist.
Belief in God without knowledge of God.
However... I do add an extra wrinkle to that of my own choosing. I consider myself a morally Christian Deist. What does that mean? Well, I don't know crap about God, but I know that once you strip away the millennia of corrupted messages and fire and brimstone that came later and focus on the basic philosophy of Christianity, it sounds pretty good to me. (Which isn't to say those basic values aren't shared by other religions, simply that it is easier for me to place it in context of Christianity culturally.)