Thank you for all the insightful comments.
What is your problem with the word "agnostic"? I believe it's the word you seem to be looking for.
The term agnostic is a useful one and I sometimes feel comfortable applying it to myself. The problem I have is that it is very broad and has some negative connotations. I think I can illustrate one of the problems this way. When I was a JW and believed in the existence of Jehovah, I still admitted to myself that I was also an agnostic. Logically, we can never know anything with complete certainty. Even if the evidence seems overwhelming, we can never fully trust that our impressions of the outside world are accurate or that our ability to evaluate evidence isn't compromised. One definition of agnostic is one who believes that it isn't possible to have certain knowledge of the existence or nonexistence of a god or gods, so I believe that applied to me, even when I was a pretty strong theist. Some people even view themselves as agnostic theists. They may believe in a god, but openly admit that they don't have firm evidence for their belief.
I'm definitely not a theist, so the term agnostic isn't very descriptive in my case. Some people view agnostics as not very interested in the question of god's existence or unwilling to expend the mental effort to evaluate the evidence. It's such a broad term that I'm sure that is true for some agnostics, but this isn't really fair the large number of agnostics that don't feel that way.