So, when I look at the LS, I always saw an alternative to the Warfare and power grabs of the galaxy. A peace-seeking, knowledge seeking group. A place for refugees, and alternative characters, because, self included, not all writers are here for the War part of Star Wars, sometimes. And the Sanctum can be that home.
With all the power-grabs and the wars going on, setting up a base for refugees (maybe a Dominion) would be a smart move.
Or focusing on a science/research without-war-profiteering center. Like a cultural center for a place to have roleplays, outsiders to visit, etc... Flagship?
On top of that, maybe setting up the LS as a place for alternative Force learning? Not everyone is a Jedi or a Sith, maybe capitalizing on differing groups, White Current, Wardens of the Sky, Zeison Sha, Jal Shey?
Perhaps making a team of representatives to travel to the galaxy and almost advertise that the Sanctum is a place for people to live free? Or that may be too much.
Yeah, rambled. But thats something I was thinking. I guess I would need help fleshing ideas out.