After a more thorough reading of this couple of comments and ideas.
Do you actually have yacht named Santini? If you do then you could use it as a base of operations. Just move it from system to system and use the allied bases for actual launching points. To me The Family sounds like a small group of rather independent pirates, so using the Santini as a base is plausible. And this would be something that sets you apart.
I'm also having problems with Vogtland being your main base because it's kinda taken and secondly (and more importantly) your ZOI is stated Omegas and Omicrons. You need to travel quite far from Vogtland to reach Omicrons. How about "taking over" Casablanca in O-47 and parking Santini there? A suitable reason for exchange for Hessian "protection" is to keep the O-47 safe from Corsair and OC incursions...
The great thing about having Santini to be your armory and base is that you can move about. You are still supposed to be on the run a bit from the OC, right?
About the age of your group. Why does it have to date back to some hundred years? There are no rumors anywhere to support it, because you don't exist really. Why not make The Family be like less than 5 years old and play it real time and see where it goes? Leaves your options much more open. This would mean that you could fly IFF-less under normal pirate IDs, but having the Hessian equipment at the moment. And with the forged deal to keep O-47 safe it would be plausible even. The Hessians are basically more or less ideological, but at the same time very practical lot too. They would not rather see you messing up Rheinland proper with your extortion racket, but they are certainly happy to enlist your men to fight the other enemies.
Rashnok is right. You should stick to your patron group equipment only (Hessian atm).
And if things are looking more brighter (or things grow sour with the Hessians) elsewhere to set up your shop, just engage the cruise engines in Santini and go and forge a new (temporary) alliance with some other unlawful group to get weps and ships from them. Nobody has done anything like this before. But to pull it off and make powers to accept this you need a solid and tight back-ground, solid RP in forums and in-game and the main idea and modus operandi which you can follow in any part of Sirius. Extortion, smuggling and piratism is good basic to build on.
Sorry if I stepped on some toes here. You have an interesting concept, but I feel it has potential for so much more than one more pirate group.
ps. Rooster = cock as opposite of hen, you might correct that before it goes to print;)