Stage 1: After not being able to arrange the display order of the "Staff" User Banner within the User Group Banners for a user, I would want to suggest that the Staff Banner does not behave different – but could also be able to set up like all other user groups.
The only difference would be that assigning a user to be "Staff" (by clicking the checkmark in his account), will still be as convenient and he will be displayed under "Staff Online" in the sidebar…
Stage 2: Another evolution to this would be to make all user group behavior treated equal – including Staff – and be able to checkmark "display group in Sidebar" in the individual user group setup. So every admin can individually setup the user groups he wants to display in the sidebar (in a certain order, depending on the order of user groups).
As an example for that, you could display two widgets in the sidebar: Topmost with "Board Members Online" and below that "Staff Online" (while "Board" means "executive members".).