Sorry I'm late to the thread, but I only just saw it now. I'll be picking some bits to respond to as I encounter them. Sorry it's a bit long; I'll try to keep my replies terse and to the point.
This gets into monetary territory, but would it be worth having regular contests for new comers to win a full copy of FS2? I'd be willing to donate $10 a month for that. It's not an idea that scales up well, but we don't get that many newcomers right now, so it might be easy to pull off in the short term.
That could potentially lead to a rash of new registrations of people that don't contribute. It might work better if it was tied to something like a new (past year or so?) user getting X upvotes on a thread or post—
if we had a thread/post upvoting feature. I would like to see that happen TBH—yes, even though I occasionally post those oh-so-controversial threads in GenDisc.

My suggestion was(and is) an aggressive push on places like Reddit, Facebook, etc. Images and videos of campaigns and other things FreeSpace related.
This. But it needs to come from the community at large, not just admins or mods or even project heads.
I'd like to figure out some way to make it basically one-click easy to share a thread, post, image on the forums, website page, or whatever on the various social media platforms. I'm thinking of something like you hover over an amazing FS2 image in a thread, and little InstaFaceTwitPin icons appear.
Now don't go barraging me with links on how to do social share buttons; I know all that—I wasn't born yesterday, and I work professionally in the web development field.

It's more a matter of getting the chance to do it.
Do you remember the pre millennial layout? With a well organised download section? I kinda miss that.
I've been wanting to have a downloads section on the website for years. Ideally torrent-based, with an Amazon S3 account acting as the seedbox (it supports torrenting files natively). IIRC, the financial cost of operating an S3 account were the main reason why we never went ahead with it. We can handle a ~$10 monthly S3 cost, maybe $20, but if it ballooned beyond that, we'd have to shut it down. :-/
I refer you to my social media comments regarding fan base attraction and maybe a pic of the day on instagram or twitter?
I'd like to throw Imgur onto that pile. It's certainly not as big as the two you mentioned, but it does have a front page that's seen by the vast majority of users, and it's relatively easy to get on (a well-curated album about an indie video game should have no problem).
Don't forget to include a banana for scale in the Colossus glamor pics.

Well you start using hastags that are vague in terms of gaming, space sims, mods and that stuff but also specific ones to your group (#freespace). Tweet your game or videos or whatever at people who do game reviews, lets plays whatever. The more people are talking to each other with and about the game, it increases the people who can see it.
This. #sim #space #spacesim #spacefighter #xwing #fighter, etc. Those are the kinds of generic or semi-generic hashtags that will expand the reach of our posts. Space sim junkies would certainly set up watchlists for at least one of those.
An official trailer which gives viewers an actual idea of what they may typically encounter when playing FSO would be an excellent way to get the game out there. However, trying to create a trailer by committee or group opinion will end up going nowhere because people are going to argue about what should and shouldn't be in it.
I still wanna see a trailer done to Hall of the Mountain King... 
I want to have a dev blog for my thing, which would be cool considering the sort of hacks I have to do to get these missions working...
Noted. I'd love to see this as well, and I have some premature ideas...

Figured this was worth a separate post: whatever we do, we DESPERATELY need a way to consolidate and standardize FSO installation instructions.
This is one of the main things the new website will launch with.
...
Really? I find it hard to believe that no one has asked about or looked for what I'm looking for, maybe it doesn't exist, but I'm persistent so ...
...
One of the first things I'd like to add to the website after it launches is an official FAQ section, with standing instructions to the community to submit entries there if anyone ever asks a question which is already answered somewhere (i.e. it gets asked more than once, into the FAQ it goes).
How about a preview of new posts scrolling by? Sort of like we have on the bottom of the main forum site, but scrolling, and floating at the bottom? (In other words, it stays fixed, scrolling new posts inside itself, while you scroll through the forums, until you pick a sub-forum, at which point it limits itself to new posts from that sub-forum).
Noted.
I may be the only one who thinks this way and that's fine for me, but getting people to sign up on the forums is the last great step for all this. People should be able to come here, find out about the game, where to get it, download mods or whatever and peace out without signing up. That way the people who do sign up are at least partway committed to leaving comments or working on their own projects.
In my opinion the less hoops we make people jump through, the better it is for getting eyes on pages. So as little effort in them getting what they want after they see it ~somewhere~ is best I think.
QFT. This is the overarching goal I have with the website.
I've added General Discussion to the list of boards excluded from Show Unread Posts. Currently, that is the only public board that is excluded.
Good solution IMO. Time will tell if it's sufficient. BTW, to all y'all complaining about how GenDisc shouldn't be the first thing newcomers see... is nobody old enough to remember when GenDisc was
at the top of the forums? We moved it to (nearly) the very bottom years ago, for the very reason that it was indeed off-topic from HLP's
purpose de existance (fake French alert).
The thread tagging feature was previously mentioned in the staff discussions. There is an SMF mod that enables tagging, and that's something I can install even before the move to the new server. Do we want to go ahead and try that out?
Yes, but is there a way for tags to be community-moderated? We don't need trolls tagging something maliciously and it having the same level of legitimacy as an accurate tag. Community moderation would be good, or perhaps something where any given tag doesn't show on a thread until X number of people have suggested it?
Here's what would work, outside the context of a forum entirely: a clearly organized, graphically simple presentation of mods with a striking screenshot and a couple lines of text each, like Apple's cover flow or Netflix's streaming presentation.
Come up with a mockup of this and I'll see about getting it into the website; while reading this thread I've been wondering how to present the various projects on the website, and this sounds at least as good as anything I came up with.

If we can't do something like the ModDB does and help everyone make their own pages that way, we really should get someone to look at those pages and get them looking a bit more professional.
We can, and it's part of what we can call Phase 2 for the website (Phase 1 being the absolute essentials to launch with, which are basically anything related to getting newbies started with playing FS2+).
Finally, I'd strongly advise
against merging public project boards. As things stand now, each project is fairly treated and has effectively equal exposure on the forums (disregarding the sorting order of the projects). Merge them all together and you're left with a forum that will have 99% of the first page be BP posts (or whatever's the most popular—I'm woefully out of date!), effectively giving all the smaller projects the shaft, exposure-wise.
Keep things separated, and figure out ways to
improve exposure of smaller projects. Personally I feel the website, post Phase 2, will go a long way to achieving this goal.