The sorts of people who would be attracted to a faction with a pvp advantage that would not be attracted to that exact faction without the pvp advantage are not the sort of people you want to attract to your faction. Most of the Das Wilde invitation process is sorting out the people who go "OMG SCORP IS WIN I want to accumulate blue messages with it" from the people who go "wow, this looks really interesting, I think I can add to it". Let's just say it's a good thing final decision goes to someone who's paranoid.
Making unique, interesting ships? Sweet! The Persephone is wimpier than a regular Juggernaut stats-wise, but it attracts attention whenever it appears. It's cool and it's presence drives interaction. The Satsuma also evokes a "oh cool" response, though it is more closely balanced to it's class. Still, it's not a Kusari Battleship, which could arguably be the "best battleship" (that's not an assessment I agree with, I hand that honor to the Liberty Dreadnought, but the point is that it's a common assessment).
Making stronger ships? Express ticket to getting all sorts of people you don't want. Exhibit A, 4.84 Cattlebruiser. Exhibit B, the Tridente. Exhibit C, the Geb (I'm aware that it dies horribly to bombers. The people who buy it aren't, and buy it because they think it's a cruiser but better.) If the Keepers were less careful about who they let in, the Turbosquid would be exhibit D (whether or not you feel that they have been careless enough to allow it to be exhibit D is not the purpose of this discussion, please don't start a flamewar on that grounds).
Something so obviously specialized as the Barge works too. It carries 25k cargo... but can't use tradelanes. Finding a barge makes for an unusual and usually quite interesting interaction, yet it isn't "superior" to normal transports- it is, after all, the most vulnerable ship in the game (Wolfhounds nonwithstanding).
Cool, interesting, unusual and rare ships make for memorable encounters. If these ships are "stronger" they tend to leave a sour taste in that memorable encounter.
So here's my suggestion... make interesting, underpowered or balanced ships that are intended to be rare, and let people SRP for them. Factions or indies, no need for an artificial stipulation- if the factions are good enough to "deserve" it they can certainly acquire an SRP, can't they? Things like Jinx's advanced Liberty warship could qualify for this. If there were only one or two of them, people would go "oh wow" when they saw it- and if it wasn't any stronger than a regular ship of its class, there wouldn't be any "stupid privileged inner circle and their pwnship toys" stuff.
What's that? You say it's special and should make a more dramatic PvP impact? The same was said of the Tridente and Geb (mainly the Geb) before they arrived, and the people who argued that have regretted it ever since. Player success is not measured in whether or not your characters can kill their foes, or if your faction "wins"- it is measured in how much fun you have.
Unique, yes. Stronger no. Also, I don't see a faction requesting a one-of-a-kind/very rare SRP ship as any different from the Necrosis, Tundra, Persephone, etc... evaluate such requests on a merit basis. No reason to artificially tell people they're inferior when you can just do things case by case.