I’m a fan of W. W. Bartley’s Pan Critical Rationalism, from his book The Retreat To Commitment. It doesn’t seem to me to fit in your list of approaches. Bartley was a student of Karl Popper, who proposed Critical Rationalism. CR, badly stated, says “This is the fundamental tenet: criticize all your beliefs and see what survives.” PCR cleans that up by saying “This is the best approach to epistemology we’ve discovered so far: criticize all your beliefs (including this one) and see what survives.”
Isn’t that better than believing in a foundational, unjustified criterion? Isn’t it more flexible than methodism? Isn’t it more useful than skepticism?
Bartley is very explicit that you stop claiming to “know” the right way. “This is my current best understanding. These are the reasons it seems to work well for distinguishing good beliefs from unhelpful ones. When I use these approaches to evaluate the current proposal, I find them to be lacking in the following way.”
If you want to argue that I’m using an inferior method, you can appeal to authority or cite scientific studies, or bully me, and I evaluate your argument. No faith, no commitment, no knowledge.