Unfortunately, Ryloth is currently under the control of an NPC organization (Mining Guild). As such that sector can only change its allegiance via the NPC alliance mechanic. Ryloth will remain neutral.
Map updated.
Even though this plot was started before the NPC factions?
@Aberforth
I am going to be talking to Nefie about this.
There shouldn't be a problem with claiming the sector or at least having some sort of influence since I started the plot before the NPC Alliance.