@RillaI've made you an Arena Mod, though the only places that's visible right now is at the top of
http://www.roleplayerguild.com/users/rilla and on
http://www.roleplayerguild.com/staff.
Your only power right now is the ability to click "Edit Topic" on roleplays in the Arena Roleplay forum.

From there you can scroll to the bottom of the edit-topic page and find the "Ranked Outcomes" panel, though the panel is only active if the roleplay is ranked.
(Obviously I will need to flesh out more Arena Mod privileges like the ability to stick/unstick/close/open/hide topics)
Would it be possible for me, as Mod, to just go through the fights and 'officially' update them?
Okay, I will add a "Promote to Ranked" button that you can access on that panel. That way you can promote a roleplay to ranked and then add the appropriate outcomes to it.
Just a sec. Update: Okay, it's implemented now.
I wonder how this'll work for multi-man fights
You can add an arbitrary mix of outcomes to a fight.
Here's an example:
