The thing about most of these 'other ways of knowing' is that they're short cuts to the same body of knowledge that reason could have given you. Most literally so in the appeal to authoritative prior sources, since in that one you're grabbing the results of someone else's use of reason (or whatever). But also many of the others: for instance, I agree that we make subconsciously guided intuitive judgments all the time, but they're all ultimately answerable to reason and subject to cross-checks by reason – and occasionally, my reason determines that some class of my intuitive judgments is persistently made the wrong way, and I have to try to adjust my intuition to fix the problem.

So these are interestingly different if you're a psychologist (because they happen by such different mechanisms) or if you're interested in the problem of getting close to the right answers under time and resource pressure (intuitive judgments, in particular, are often used when there just isn't the time to sit down and reason formally). But when the topic of discussion is whether or not there's a god and related questions, which is something we have our whole lives to sit down and think carefully about, the only interestingly different 'other ways of knowing' are those (if any) which access a region of reality that is inaccessible to reason, not those which take short cuts to places that reason would have got you to eventually.