Analytic and Synthetic in "Two Dogmas"

I recently reread Quine's "Two Dogmas," and I found myself with a question.

In "Two Dogmas" Quine argues that there is no principled line to be drawn between analytic and synthetic judgments. After dismissing several other versions of the distinction, he caches out synthetic judgments as those that are confirmed or dismissed on the basis of experience, and analytic judgments as those who truth or falsity are determined independently of experience. So "All bachelors are unmarried" would be analytic, since no experience could change disconfirm that sentence. All experience is irrelevant for the truth of the statement.

Anyway: The way I read him, Quine argues that any judgment can be preserved independent of all experience. Take the proposition "My computer is making funny noises right now," which, sadly, I take to be a truth. Reductionism would claim that there is a partition of experiences into those that confirm my proposition, those that disconfirm my proposition, and those that are irrelevant to my proposition. But there's very little forcing me to carve up experiences in this way. Say that I hold the belief that God is a deceiver, and that he is systematically making me hear things that are not actually being sounded. Well, then my experience of hearing funny noises from my computer isn't really relevant any more to the truth of my proposition. How you classify experiences depends on all of one's other judgments, so that carving up experiences in this way is folly.

As a consequence, I can maintain the belief in any proposition in the face of any experiences. I just have to change something else in my corporate body of beliefs.

OK so far. But it seems to me that someone committed to the analytic/synthetic distinction could easily bounce back from this. Conventionally, it would never be appropriate to change one's belief in an analytic proposition because of experience. After all, "All bachelors are unmarried" shouldn't depend on experience in any way. So just stipulate that analytic statements are those that are never confirmed or disconfirmed by experience, and synthetic statements are those that are capable of being challenged by experience. Or something like that.

Now, I do understand that this doesn't touch Quine. Quine believes that logical and "linguistic" truths really could be challenged by experience. It would be appropriate to revise one's logical beliefs, for instance, given a challenge to the theory. Anything is fair game. Quine's argument against the analytic/synthetic distinction is buttressed by his fallibilism.

What I found myself wondering is, could there be any way to continue the challenge to the analytic/synthetic distinction without invoking the fallibility of our logical and linguistic beliefs? What would it look like to reject the fallibility of our logical beliefs as well as the analytic/synthetic distinction?

I need to think about this some more, especially since I think I just am beginning to understand what fallibility entails. This was a messy post. Sorry!