Thanks for engaging in the conversation. When I say "the justification is faulty" I just mean it's not deductively air-tight, therefore we can't assume that it leads to truth. In this sense, pretty much all justifications are 'faulty.'
The thing I'm struggling with here, ultimately, is truth. All of these problems rely on some outside, oracular knowledge of what is true, (e.g. in the example you linked there really is a cow/sheep in the field, or Mark is really hiding under the desk). But we have no such oracle to refer to, so trying to ground knowledge in truth seems like a lost cause in the first place. All we can have is more or less certain beliefs.
Sure, from a present perspective on epistemology this may make sense, since we now know all the troubles and faulty attempts to decide proper justifications from incorrect ones after Gettier's paper. However, back then the idea to define knowledge using JTB was on the table. The knowledge as justified true belief view is about a definition of knowledge, not a learning method or how to gain knowledge. Many authors would even have rejected the idea of graded belief entirely and said you either believe something or don't (many still do).
Since you accept the notion of truth (otherwise you couldn't be a Bayesian), you'd have to explain why you reject the realist conception of knowledge inherent to the JTB view. Gettier's paper is one attack on it, arguing for graded belief representations is another type of attack on it. In this context it is worth noting that graded belief and categorical belief are very hard to reconcile because they have different logical properties [1]. It's known as Locke's Thesis and quite a vexing problem.
That being said, I share your intuitions. The factivity of knowledge has created more problems in epistemology than the notion of knowledge was supposed to solve. The German word Erkenntnis in Erkenntnistheorie has a meaning closer to learning theory. AFAIK there is no good equivalent to this in English.
The thing I'm struggling with here, ultimately, is truth. All of these problems rely on some outside, oracular knowledge of what is true, (e.g. in the example you linked there really is a cow/sheep in the field, or Mark is really hiding under the desk). But we have no such oracle to refer to, so trying to ground knowledge in truth seems like a lost cause in the first place. All we can have is more or less certain beliefs.