As someone who has only passingly lurked here, eating up the meme threads, for years, only actually registering a couple years ago, and only choosing to actually get a bit more involved days before the precipitating events happened, I speak very much as an outsider to HLP's culture. Take it for what that's worth.
Fineus and RazorsKiss make some excellent points about how to use social media to the community's advantage. I found HLP because a friend who'd been here for a while pointed me here after they'd found something entertaining and thought I might like. That's the power of the network effect: your friends to tell their friends, who read something interesting or funny, who then share it with their friends on social media and maybe get curious and decide to dip their toes in. That's how D&D has become a cultural juggernaut again, not just the monolith of a niche hobby it was 20 years ago. It'll work for HLP, too. In specific, what my friend introduced me to HLP with, and what convinced me to check back every few months, were some of Battuta's...idiosyncratic dev diaries for War in Heaven. I think those kinds of threads -- weird and wild tales from the modding mines or just plain interesting technical hurdles from the SCP (that one time ShivanSpS found out ModelView had been stripping needed padding from model files for decades, causing memory issues on ARM systems comes to mind) -- would be great to add to the social media feeds. While they don't really go viral on a world-wide scale, they to tend to get passed around in the special-interest groups they're relevant to.
As someone who hangs around the Twitter art community a lot, retweeting old posts or pulling old content "from the vaults" is a great way to shore up your feed when you don't have anything new at hand. Posts on Twitter, by design, are transient, and very few people will see them more than a couple hours after the posts go up unless they get a lot of engagement from other users. Retweeting and reposting moves stuff back to the top of the pile and it's really effective, especially for reaching audiences outside your timezone who may've missed it because they were sleeping or at work. I vaguely recall there being a "Best of HLP" thread somewhere, but if there isn't, going back through the archives, putting one together, and keeping it curated would give the social media team a good resource of classic content to draw on during periods of low activity. Screenshots of conversations in the Discord absolutely qualify for this as well.
Speaking of, one of the most important things for capitalizing on the network effect is "low barrier to entry", and Discord is a fantastic way to do that, since it's supplanted Skype, IRC, and in-page chat boxes for communicating with internet friends and communities. Since most people have a Discord account already, joining a server and getting involved is just a matter of clicking an invite link. Compare to the "antiquated" effort of filling out a registration page, coming up with a new password, waiting for the validation email, and then figuring out which forum thread you want to use to make your first impression and coming up with a suitable post that doesn't make you look like a random hanger-on. For someone who is just curious, they may not get to that last part. Making sure that lower-cost option is put in front of everyone who interacts with HLP's output -- be it social media, Knossos (as Matth suggested), or even the forums themselves (see Mobius) -- will give potential new community members an easier, more comfortable way to get situated.
On the topic of rules, re-evaluating the forum rules is absolutely important and should be done regularly as a way to monitor the health and direction of the community. Maybe annually would be a good interval. However, revising the rules so they're "less likely to be gamed" is the wrong way to approach this. Rules being gamed is often symptomatic of a prolonged and focused enforcement of only the letter of the rules, not their spirit. "The rules don't say I can't, so I'm gonna." Mainly, the spirit of the forum rules, like most rules, boils down to something rather simple: "Don't be a dick". But, this is the internet, we're all cranky and...if not necessarily friends, at least want on tolerable terms with each other, so a certain level of dickery is permissible. It's up to the moderation team to decide what level of dickery they're willing to put up with and let others put up with. However, there needs to be a structural commitment to enforcing that level in the moderation process. If someone's conduct isn't breaking the rules-as-written, but is still quite obviously causing a problem, that conduct needs to be corrected, rules or not, and it needs to be corrected every time. Enforcement of the rules doesn't need to, and in fact shouldn't, hinge on technicalities to be equitable. Even real world black-letter law allows for a fair bit of judicial discretion and the stakes on an internet forum are far, far lower than those of real world crime and punishment.
To be less brutally utilitarian about it, the spirit of the rules should also reflect the kind of community and audience we want to build with HLP, the kinds of interactions we want to to define the board and present to the outside world. There's a saying that you get the audience you build, and if you don't try to build it, it will be built for you. And odds are it'll be the dregs, the people who are too short-sighted, too toxic, and too stubborn to see how their behavior impacts others, to acknowledge or make amends for wrongdoing, who have decided this is their town because it's the one they haven't been chased out of yet, and ultimately drive away the people you want to have around with that behavior. I've seen it before, and the communities who let those kinds of people stay around tend to end up so consumed by Petty Fandom Drama that nothing else gets done.
Building a community is in many ways a proactive activity for the moderators. It's not just a matter of smacking down people who cross a line and then going back to sleep until the next time a problem arises. There needs to be a consistent effort to promote the the kinds of conduct the staff wants to see in the community. Often the staff will need to lead from the front on that, conducting themselves (as much as is reasonable, given that they're human beings with lives and problems outside of HLP) in the manner they expect members to. If the staff has standards of critique for mods or writing, they need to proactively make critiques that meet that standards as models for other members to follow. Problem behavior needs to be addressed early before it spreads. Staff needs to check in on people -- especially new people -- who have been made uncomfortable by problem behavior. That last one is more important that I think a lot of people give it credit for. It's the difference between "I'm not sure I belong here" and "These people want me to belong here", and that is massively important for member retention. It's an unrealistic expectation for staff to give every person who visits the forums or the Discord a laurel and hearty handshake, pull out a chair for them, ask them what they want from the bar, as nice as that kind of personal service is for welcoming people to the community. However, staff taking the time to check in on someone who has been upset by problem behavior changes how that person views the staff; the staff is no longer just concerned with punishing the guilty, the staff is also aware of the effects those offenses have on the community and the need for those effects to be addressed. And that shift in perception is a powerful, powerful force for making people feel welcome.