Judicial Order

[Haste]

Try coming in as what you really are, a new group.

I'm just going to second this once more, as I really think this is the best way to set up your faction. I think retconning should be avoided if possible, and well.. For all intents and purposes, it is possible.

Another interesting fact is that your ingame behavior is nothing like the behavior I'd expect after reading your lore. Your in-game attitude most certainly isn't one of a military, ex-military or even paramilitary organization.
Quite often, five or so of you remain parked on Newark while New York's being overrun by unlawfuls - or, more recently, docking on Newark at the sight of something that may attack you. As Freelancers, nothing is stopping you from either making use of the bounty boards you have managed to sign up for, or simply offering your aid to the lawfuls nearby - for a price. Being outnumbered, it'd be unlikely they'd refuse your help.
Frankly, you seem to think that until you get official status, you should park on Newark to accumulate activity time. Then, after you get your status, you'll suddenly go around and act the way your lore would dictate?

Maybe you should consider talking to the factions whose lore you're trying to alter - the Liberty Navy, who you apparently are a predecessor of. Ageira, whose technology you allegedly safeguarded (although this one's hard as they're not an official faction at this point). And, given the Sirius-wide relations you claim to have: pretty much every other military organization or security force.

Nothing's stopping you from actually "playing out" your lore.