I work part time for a youtube channel with over 500,000 subs as a video editor. I'm a huge fan of the FFT series and what this site has done for it and I would love to help it get some proper appreciation.
You could do a walk / playthrough of one of the hacks. CoP ch3 is out and JoT5 (though it's only one chapter) is awesome.
Promoting the website/community itself wouldn't do us much good... there are far more people interested in playing mods than creating them (It is SO hard to get ANY help for modding no matter the amount of interest; it's depressing).
Unlike Jumza, I will go against doing walkthroughs/playthroughs... what I would instead suggest are promotional videos. Because, after all, you're a video editor and not a let's player.
Journey of the Five
[indent=2]The team has been speaking about it for some time though, and it would be wonderful to have a promotional video at least for the re-release, if not the chapter 2 release. We already have some very good ideas of what to show, but none of us has any worthwhile experience in video editing... It would normally fall on my hands, the do-it-all of FFH and JotF. But if you could take that off from my list, that would be great! I'm a perfectionist and inexperienced, so it would take me a ridiculous amount of time by myself. If you are interested and Elric agrees, we can fill you in on the details and give you a workable patch before the official release so that you can do your magic. Obviously, that's not right now, but hopefully not in too long either.[/indent]
Any other playable mod
[indent=2]I can't speak for many mods as I'm really focused on JotF; I just try to help where I can. I know some things can be really bad for publicity (like emulator-only because of bad ASM hacks), and some catastrophic (ASM hacks breaking the entire game). The former happens to nearly every mod, sadly, and the latter still happens to a too great number of mods (see FFT+).[/indent]
In the end, I would say go for the mods you want to promote the most... but it will likely require you a full playthrough's recording at the very least regardless. :p
What Xif said, while LPs aren't bad (lord knows how many downloads Jot5 has had due to LPs) it sounds like trailers/promo videos would be more up your alley.
/me approves of all the things