I agree that the signal being sent is coarse-grained.
I agree that finegraining it is a lovely thing for people to do if they can do it in a way that's low-cost to everyone else.
I disagree with your implicit separation of signalling community (dis)approval on the one hand, and reputation costs on the other. The reputation in this case is precisely a function of community (dis)approval; I don't see how you can sensibly separating them. If I endorse explicitly signalling community (dis)approval at all (which I do), I can't help but endorse explicitly raising/lowering reputation.
My only concern with the FAQ approach is the question of what an individual voter whose reasons for (dis)approval don't align with the FAQ ought to do. If I'm understanding you, your idea is that the FAQ trumps the actual preferences of people in the community -- that is, I'm expected to vote in accordance with the FAQ rather than my own preferences. That makes the existence and contents of the FAQ an implicit power structure, and such things are best approached with caution.
That said, I don't object to it if so approached.
I don't understand the disagreement with splitting the reputation. For example, a really trivially easy way to do it would be like this: On every post, have a thumbs-up/thumbs-down vote button that is specific just to that post, and then have a separate thumbs-up/thumbs-down button that appears next to the name of the user who made the post.
If you just dislike that particular post because it is off-topic, but you think the poster had the intention that it was on-topic (you just dispute that they were correct in their intention), then just downvote the ques...
This is interesting, I wonder if there's anything to it: International variation in IQ – the role of parasites (paper) by Christopher Hassall of U. Carleton.
It strikes me as the sort of thing that could be as big an issue as lead in the environment. Raise the sanity waterline: improve health!