I like the concept (however unoriginal) of a professional group of mercenaries who are basically a PMC, it's very fitting in the FL universe and if you're able to get some history and RP written behind it, all the better.
However, I rather dislike the idea of using Core capital ships, mainly because Core capital ships are manufactured by the Core, for the Core, and are not sold to third parties, no matter how well paying they may be. I mean the idea of using a Battleship as a mobile base and whatnot is fine, it's just that I don't think Core capital ships are the right choice at all.
Aaaaaaand as far as I know, the one faction per official faction rule isn't up for debate, especially as it has been the end of several much better factions in the past (not a judgement on your quality, just some really cool faction have been swept aside by it).
Also, no, the Bounty Hunter ID is not generic IIRC.