Since the others have been quite thorough with reasons NOT to use the SCRA ID, I don't feel the need to repeat what the others have said.
With regards to things you can do to make your faction work with the powers that be, I'd suggest boiling your faction down into the bare minimum of what you WANT to be able to do and go from there - story can be adapted to fit afterwards.
If you'd like to participate in fighting unlawfuls throughout Sirius (with exception to Rheinland, which you are apparently hostile to), a Bounty Hunter ID should do. the Bounty Hunter ID is considered pseudo-generic, if memory serves - but even if it isn't, you can always start from there to establish yourself as a lawful combat force. Of course, you'll have to register yourselves on the bounty boards for the respective houses that you want to work for, but it's the only way that you can go about shooting all unlawfuls you come across without having a particular faction ID (unless you get a pirate ID).
Another option is to run with a pirate ID, and restrict yourselves only to unlawful targets - you'd have to have a good chat with the lawfuls that run the respective houses that you want to operate in, but they tend to be reasonable folk. Of course, you'd be limited to docking only on freeports and freelancer bases, since lawfuls won't let you dock by virtue of rephack, and unlawfuls would not let you dock due to your anti-unlawful RP.
EDIT: Oh, I forgot to mention that you could operate with the freelancer ID too - though you'd still need to participate on the bounty board.
Though, I'd probably recommend running with the pirate ID since it allows for most of what you want to do. You don't necessarily HAVE to pirate, so don't be discouraged by the name of the ID. You can take a look at the RP that the VR is doing with Liberty to have a peek at how to conduct diplomacy in houses that you want to work in. Still, lawful bases and lanes will be hostile to you via rephack, but if you play long enough and contribute enough to the mod, you MIGHT be able to request for your own ID. It worked for the Mandelorian Mercs and the Reavers, so don't get too discouraged.
