Suggestion: PvE base raids.
Make it a supergroup team mission, where the base has to be defended from several waves of NPC enemies, ending in perhaps an AV/Hero attacking the base. Use the current GM level code as it is applied to Rikti during the invasion, so that all members can contribute. This could be a part of a trial or task force, or a spawnable event all it's own. It would allow one SG do it's own event witout the need to schedule with another group of players to do the raiding, and allows players who don't enjoy PvP to join in on the fun, and makes bases more than just a transportation hub.