1. Recruit more flairs/experts! We need depth: sometimes multiple questions are "live" simultaneously on very similar topics, and the flair or flairs in question (along with not-yet-flaired community members) don't have time to answer them all to the level that we like to. We need breadth: there are many questions where AH simply doesn't have anyone who can answer them knowledgeably!

2. OP mentioned that they do this, but for other readers: browse /new and upvote interesting answer-less questions! If I'm going to take the time to write 1000+ words of history on the Internet when I have fifty thousand other things to do, I'd like to know that more than one person will read it.

3. When you read a good answer, upvote it. I've talked with a few people about this and we agree that we don't really care about karma as numbers: we care about it as a proxy for readers. Sure, I've poured out my heart on a few answers that are near and dear to me for like 1 Ego Point (and I will continue to do so), but upvotes make me feel like I am actually reaching people and accomplishing something. If you feel awkward about karma, we also accept "Thanks, that was a really interesting post, mind if I ask a follow-up question?" :D

4. Read the less-upvoted threads with an answer, and demonstrate that you've read the answer by upvoting (thread + answer). Don't just read the threads with 1500 upvotes and 86 comments because "it'll have good discussion."

5. If you have a pattern of asking questions that go unanswered, try PMing a flaired user in the field or fields you're interested in. Check the flair profile page--many of us have "PM me!" in our profiles. We're always thrilled to help you come up with a way to word a question that makes it compelling to answerers as well as readers. :)

I very much support what /u/sunagainstgold wrote below, especially about getting people engaged in providing quality answers and paging or pming users (I am always up for that)

Another thing is though that not all questions can be answered. In my field of expertise some of the questions can't be answered because there - for example - are no sources about what Hitler's favorite tank was or what he thought about brussels sprouts (educated guess: he hated them). Sure, there is the possibility of giving an answer going into detail about why it isn't possible to give an answer and these can be very interesting to write but sometimes, just the only possible answer is a simple "no" or "we can't say". And those are really unsatisfying to write and impossible to answer with the depth required.

The fundamental problem is that AH is, and always will be, a volunteer group. If no one exists in the community who knows the answer, you are out of luck.

Beyond the basics, PMing users with relevant flair, etc... the most productive things you can do to improve the breadth of questions that can be answered are to a) find a topic that interests you, and become an expert and flaired user yourself, b) encourage a friend or acquaintance you know who is an expert to participate, c) continue to ask questions about esoteric topics, because sometimes flaired users 'retire' because they don't see enough questions in their field to stay interested.

I'm not an answerer of questions, so how well this would work depends on the habits of people who do regularly answer questions.

But why not have a subreddit (approved submitters only) or wiki page specifically for unanswered (and unarchived) questions, in an easy-to-read list format, organised by topic? Have mods update the lists every day with those posts that have fallen off the front page without answers. A knowledgeable user who feels bored can look through the section pertaining to their expertise at any time to see if there's anything that strikes their interest.

Downside would be that it would require a lot of bookkeeping work. You'd need people to go through every submission every day to check for answers, to update the lists, to remove archived posts from the lists, to remove posts when they received answers (how would anyone know? Maybe include instructions, "if you answer a question you find on this list, please tag the designated mod, so that we can remove that item from this list"?).

I think it needs to be recognized though that quite a few questions asked simply don't have good answers available. History, contrary to popular perception, is not set in stone nor omniscient. There are very large gaps in our knowledge especially the farther back you go into the past.

Unfortunately there usually isn't a good way of answering these "we don't know" questions; and they remained unanswered in the slim hope somebody actually did some research on a particularly obscure topic. It's kind of embarrassing to say "we don't know" and then have someone show up with a particularly obscure source that answers a question for instance.