As one of the old BHG|, MM~, Reavers, and a whole lot of generic mercs over the years, I have to say this is not that good of an idea.
Pvpwhore-wannabes are better off in merc factions, and it's not meant as an insult, just an observation. It's the play style that defines the role, and people behind the character are the ones that define the play style. The old BHG| had a more laid back approach at bounty hunting and PvP, and even though there were a considerable number of decent PvPers in the faction over the years, they didn't put PvP and blues at top of their priority list, and actually focused on playing a bounty hunter, rather than just collecting bounties. Based on the numerous run-ins I've had with Faze, Blaze and the general Reaver copycat population over time, they all appear to be PvP oriented factions (which is not essentially a bad thing, but) if such play style is incorporated into the BHG|, it'd turn them into yet another gang of trigger-happy gun-for-hires with no distinct feature of their own.
To represent the official bounty hunter faction and to act as an example for every other hunter out there, you'd first need to reconsider your approach at hunting bounties. As things currently are, your group and groups similar to yours aim to post as many blues on boards as possible, and even though there's nothing wrong with that and that's why we have hunters in the first place, an official entity representing the main bounty hunting organization of vanilla needs to be more than that, and needs "hunter roleplay" on top of "hunter gameplay" - not just on forums, but ingame as well.
tl;dr - No offense to you bunch, but your play style does not suit anything more than a small-time merc gang, as you currently play. BHG| (ideally) needs to be more than that, and while your groups have only been active in "hunter gameplay", a BHG| faction needs to contribute to the server and the community with "hunter roleplay" on top of that.