So I recently found out something that likely helps.
I handed in some bounties at a station where the guys issuing the bounty (ie. the faction hostile to you) were NOT present and as soon as I did my reputation increased from "Hostile" to "disliked".
How I got this bounty target initially was, while in the system owned by the hostile faction, I destroyed a wanted ship NOT belonging to the hostile faction.
What this means is that this is an avenue to use to raise your rep with that hostile faction even if you cannot interact with any contacts of theirs at any station/settlement where they are present.
I handed in some bounties at a station where the guys issuing the bounty (ie. the faction hostile to you) were NOT present and as soon as I did my reputation increased from "Hostile" to "disliked".
How I got this bounty target initially was, while in the system owned by the hostile faction, I destroyed a wanted ship NOT belonging to the hostile faction.
What this means is that this is an avenue to use to raise your rep with that hostile faction even if you cannot interact with any contacts of theirs at any station/settlement where they are present.