The biggest issue with the Omegas is that it'd kill ready access to several of our most important historical connections. We'd lose access to the MRG for all practical purposes - Gallia was the reason we were able to get pardoned to begin with. Yes, that's a hostile connection, but still an important one. We'd be too far from the Outcasts, who are important for VR history. We'd lose most access to Crayter, who helped us out of the initial mess we were in upon returning. We'd lose access to Liberty, but truth be told I'm not big on the Land of Endless Dreadnoughts so that's not as big a deal.
Moving to the Sigmas would preserve the Outcast connection, but lose Bretonia, who we've taken an interest in regarding the Gallic menace. Either would give easier access to the Bundschuh and Hessians, important recent-historical allies, and access to Rheinland, a useful historical target, The Omicrons are squid territory and I'm not about that.
I'm still against moving, but I do see merit to the idea and have concepts for ways to explain why we moved should we go that route.
And, no, there's not an existing ID that lacks an official or near-official faction that I'm actually interested in. As far as I can tell, most of the missing ones are corporate, which bore the hell out of me.