Rather than "I believe" or "I know", my beliefs could be best described as "I don't care". That is: "Since an omnipotent god is by definition unprovable, I can't prove gods do or do not exist. However I have no interest in unfalsifiable propositions, and so do not care about/have no interest in gods and their religions".

That doesn't really fit into the two-axis belief system you've described, and I think generalising beliefs in such a way is likely to cause confusion by over-simplification.