Already spoke to a DM about a few ideas, simply posting them here as a reference, and adding a few new ones.
Free resting in the Clan Hall.
Give the Armsman Key something to open.
The ability to 'un-wand' and remove Bannersman from the faction.
Able to access certain rewards with a DM clearance to reward PC Bannersmen for deeds that aid the clan.
You can remove Bannermen from the faction by subduing them and taking away their key and uniform. They will effectively gain no benefits from the Clan any longer, as wages are linked to the uniform.
I do think that the Armsman key opens up an additional floor within the Estate, no?
A special shop for the higher Clan hierarchy, meant to reward promising Bannermen with, does indeed sound like a good idea. Of course, the items sold shouldn't really be of any particular use to a competent Arsman, but perhaps useful to a new recruit.
I concur with Jagged the ability to remove people from the faction should be beating ass, and taking keys.