Thanks for your very lucid and sensible post. As usual, I couldn't agree more with almost everything you said. The only thing I'm not sure I agree is your requirement for God to be sentient. As you said, nobody has a clue what they mean when they use the word 'God' so I feel free to make up my own definition. I'm interested in learning what you think of it.
In my understanding God is, to most people, a very fuzzy concept which expresses a very subjective idea. The concept might be fuzzy and the idea entirely subjective, but since we all share it we can talk about it. The idea goes alone the lines of "does the universe care about us or not?". Given the amount of information we currently have, it's impossible to answer that question (even though people like Alex and Jisbond will insist on the contrary). So for a rational person that has no sympathy for dogma of any kind, the only possible answer is "I don't know, but I may find out someday".
I think people almost always lose sight of the meaning of the word "believe". Essentially, when a person says "I believe", he or she is simply saying "as of this moment I do not and cannot know, but it is my desire that it be true". It is in that sense that I say I believe in God, I'm fully aware that we do not and cannot know whether the universe cares about us, but it is my desire that one day I will find out that it does. So unless a person doesn't enjoy being alive, doesn't look forward to self-extinction, and is not foolish enough to believe there are no more mysteries left, I see no reason at all not to believe in God. From my understanding of what believing in God means, an atheist can only be a very pessimistic person or, most often, a fool who thinks he knows everything.
I'm sure that that is what most people have in mind. The fact that we know very little about the universe opens the possibility that it does care for us. Despite all the strife, we have plenty of reason to celebrate the fact that we are alive, and it's only natural to suppose that there's a good chance that that joy is not the result of an accident. That's really all there is to believing in God, for as long as people are happy and not ominiscient they will say they believe in God. It actually strikes me as odd that a few say they don't.