Wouldn't a simple Left side/Right side list of clan members be the most straight forward way to organize this? Steel Meridian, Arbiters of Hexis and Cephalon Suda being the left side while Perrin Sequence, Red Veil and New Loka are on the right.
I know not everyone would fit neatly into this, but allegiance to either side is really determined by who you've pissed off most, rather then who likes you.
For example: The most efficient way to maximize possible rewards involves starting with either Steel Meridian or Red Veil. Depending how you go about this, you will annoy 2 factions from one side more than the other... Ideally you will then switch to the side you annoyed least to minimize the negative advancement "sacrifices".
In my case, I have maximum allegiance to all 3 factions on the Left side while also having favor with Red Veil (mostly to get the Large Ammo Restore), despite never wearing a Red Veil Sigil.
Also, all the rewards are viewable in-game! So the most pertinent info is Left or Right! Right?
Edit: BTW, I hope to trade for the New Loka Sancti Castana and Bright Purity, and the Perrin Toxic Sequence! May be tough though, as I sense there are more ppl allied to the left than the right...