The best way to get more engagement is write better posts (or posts of more interest to the LessWrong audience). Looking at your posts, they're getting the reception I'd expect on LessWrong for their quality and interestingness. The tone/genre isn't quite standard LessWrong, and from a quick look, they're not obviously saying something novel. If they are, I'd have to work to read it.
There aren't stated site rules rules for everything (hard to think of in advance) but publishing/unpublishing/republishing (unless there are very substantial edits) are not things I think we'd allow, so better not.
I agree that spam can negatively impact a site, but if my posts is only being seen by a couple of people and are still getting upvoted, I do not see the issue with reposting provided I edit the post a bit and wait at least a day between posts.
I also do not understand how the whole front-page/ personal blog distinction works, which makes me think once again only a few people are actually able to see certain posts to begin with.
The strategy is selecting specifically for amplifying the most unpopular posts. Doesn't that strike you as a poor way for the site to work?
Now imagine if everyone did this. Everyone would like more engagement. We'd have many times as many posts to sort through as everyone posted everything multiple times. And even less idea which are most worth our time, because there would be multiple sets of upvotes. And there would be multiple sets of comments.
This is so obviously a bad idea that I don't think there's even an official rule against it. I would definitely expect you'd get banned if you did this multiple times.
How the personal blog post/front-page distinction works: all posts start as personal when they're first published. Then a mod goes through and looks at all the posts. They promote the ones that meet the criteria for the front page (unless the author unclicked the button saying "mods can promote to front page"). Then that post is on the front page. This is a manual thing and happens at different times.
I have several times posted at an awkward time, and had my post probably fall off the front page (how the algorithm handles time seems to be unique to each user; if you don't read frequently, posts "decay" slower so you see the best of the last month; if you're on every day, the front page feels more like the best of the last two days). This was really disappointing for me because I'd spent literally months on those posts. I did not repost them despite the argument that they'd been unfairly passed over, for all the reasons above.
When to post: a few hours before 10am Pacific time. That's not a hard rule, but it seems promotion to front page tends to happen around then. This rhythm has changed recently, and it happens more on a rolling basis, so I'm not positive that rule still holds. This typically gives your post the maximum time on the front page.
Thanks for the advice. I guess I can see why some would be opposed to this, although personally I would not mind if people reposted more often (perhaps a good middle position would be to bar reposts from making the front page until reaching a certain karma threshold). I think I'll leave my reposts up, as I unpublished a couple of my originals. Nevertheless, LessWrong should make its guidelines on reposting clearer, because I did not see any rule against this, and could see myself continuing to repost if I did not ask this question.
I've had a couple of instances where I posted something that didn't get much engagement, so I edited it slightly and reposted a few days later. When I do this, is it better to just make a new post with the same content, or unpublish the old post and then republish it? The latter would start with more upvotes, but also potentially be older, so I am not sure how the ranking algorithm would treat it.