No, without epiphanies you probably shouldn't be more than 95% confident, I think; with the institutions we currently have for epistemic communication, and with the polarizing nature of the subject, I don't think most people can be very confident either way. So I would say yes, I think between 5% and 95% would be appropriate, and I don't think I share your intuition that that would be fairly surprising, perhaps because I don't understand it. Take cold fusion, say, and ask a typical college student studying in psychology how plausible they think it is that it has been developed or will soon be developed et cetera. I think they should give an answer between 5% and 95% for most variations on that question. I think the supernatural is in that reference class. You have in mind a better reference class?

I agree the response you propose in your second paragraph is good. I don't remember what I was proposing instead but if it was at odds with what you're proposing then it might not be good, especially if what I recommended requires somewhat complex engineering/politics, which IIRC it did.