Let's all be philosophers who look "at how to reconcile how much in our daily experience we trust beliefs we get from knowledge and the philosophical intuition that those beliefs do not constitute knowledge proper."
Perhaps your question asked about an existing philosopher who has done this because your interest in philosophy is heavily tilted toward a reliance on authorities ;-).
When I heard that Socrates made the claim that we cannot know anything, I liked that claim. I have taken it up as my own claim as well. What we can do is define things, and if we provide definitions that are simple enough, then others can use the same thing in the same way and we can achieve some agreement. For example, we defined 2 and + and = and 4, so we can agree that 2+2=4, and we all "know" what it means. Well, we all define what it means. But we use the word know to mean something, and we would be well served to be more honest about it. That's what I think your question seeks: honesty.
I have three children. They and my wife used to ask me if I was sure when I answered a question, sometimes. At first (and probably long before I got married), I would put a sureness-measure on my answer: "99.44% sure." Since I liked math, I imagined I was saying that the present circumstances could present themselves ten thousand times, and I think I'd be right in all but 56 of them. I suppose that I have decided that I will claim knowledge when the chances I estimate of being wrong are one in a million, though ten thousand also seems big enough, to say I know it. I still say I'm sure when it's one out of a hundred or more, but by now everyone I talk to knows what "I'm sure" means when I say it.
Ok, so let's reconcile authority with knowledge. There are two kinds of authority, one of which is actually fake. The fake authorities say "It's my way or you go to jail." They use brutality and violence rather than reason. They suck. Can we say that here? Well, they do, and that's why. The other kind is people who study so much that they're aware of a lot more in a particular area than the rest of us. If they disagree with what we say about a particular thing, they're probably right because... they're an authority. The reason that's a fallacy is that probably isn't good enough. To be good enough, you have to go through all the work the authority did (and if they did it well, that shouldn't take too long).
Fallacies are dangerous, but most people learn that they've used a fallacy by suffering (not dying), so they aren't all that dangerous. The fallacy of appeal to authority is difficult to see (but it's getting easier because of fake authority) because most authorities (but see my previous parenthetical) actually do pretty good work. If they use threats instead of reason, then you can write them off. Knowledge does not come from coercion.