I could only tell you how we deal with those issues within OSI and the Vagrants. Both factions have very special traits that make them unique. OSI has the smallest 5k trader and is the only faction that can use it in the most economical important systems, the Sovereign House Systems. If people don't play along our rules, they lose that priviledge. Similar with the Vagrants. We have a very nice ID and technically access to ships not everyone can have. If people don't play along our rules, they lose that. That aspect won't help you with the UN|, I guess, as there are better IDs out there and you don't have unique boni that make the UN| interesting. However similar to LH, the Vagrants an internal economy. We have our Evolution Point Scores, where people can show off their blues. While it is less used as something to compete with other Vagrants, so far, it is used to rank up. That encourages our people to not just log for group raids but also roam around on their own. They not only get points by killing, but also by watching other people in radar range killing, and they even get one point by getting killed - with other words, even if you are as crappy as I am in PvP, you shall not suffer from it. Of course, if you are good, you benefit from it. Apart from that, it encourages our people to tag along with allies and watch them fighting reds. So with that, we have already one thing to ensure our people log on their own and sometimes with our good inRP friends, the Commune.
Additional, like Core| and LH~ have it, we have our set of trials. Those need to be done additional to the gathering of points. The trials are there to ensure we not only have pew pew, but also other aspects. Exploration, fighting NPCs, RP ingame, RP on forum. We guide our newbies by the hand and show them how to do the forum stuff via templates and tutorials and references. With other words, our peeps, even while they aren't that many, do many things and don't just log for pews. I mean, they even have to do stuff to get the only good ships the nomads currently have, the Rabisu and the Marduk. Our newcomer Felsvar earned his Rabisu already and is now working on the other path to get an Irra, the same is Freelancer veteran Wasserdrache doing, too. And I love to see their progress.
What you should do is, as your faction doesn't have unique stuff, give it unique stuff. Credits can be transfered from everywhere, equipment the same. People don't need the UN| ID to fly around with Vidars/Hels. You need to find something finite. Internal scores and internal currencies. People love rare currencies and commodities. If I was you, I'd make up something for a new ranking system and aim for something materialistic for the long run, something you maybe can get via the Faction Perk System, if that is still a thing. I could imagine you can get someone to paint a bunch of emblems/medals people can achieve in the UN|. The brown bunny!
Just keep up the good work then, and don't give up. There will always be some down-phases. Just wait it out, do what you usually do, show some presence every now and then and people should approach you sooner or later.