So I figured out, a little too late perhaps, that I could use one of my fake identities to get us down to the planet. Despite my departure for the empire, it was still solid. Too bad we already spoke to this guy. So, we made up a lie about leaving and returning at a future date once we got clearance. Then we left the system, waited a day or so and re-approached the planet from a different route, submitting a different ship ID. Dammit, it was the same guy, who thought everything was highly irregular. We were surrounded by escort fighters, so I pulled rank and demanded to speak with the guy, Jaxon, personally and ream him out. Hopefully, he would back down and let us through.
Turns out it was all for naught, because he was a sleeper of the cult we were trying to see anyways. So, he let us get down to the planet, and after landing a little ways out from the cult's compound, we trekked it there on foot. They eventually let us in (they were expecting us, after all), and we found out more about them. They were Revanites, followers of a Sith Lord from a couple of hundred years ago named Darth Revan. He apparently has some crazy back story, skirting the line between the light and dark side of the force. Indeed, many of the cultists are members of both the Empire and the Republic.
Our main contact was a Sith pureblood named Atronis, and she gave us the pitch to join their group. They seemed interesting enough, so we agreed. Atronis was to be my mentor for this period. It would be a long road, and there were several people in the encampment who have been trying to become full members for several years already.