Well if you want something different for ANBU Neji, then how about this for an idea:
"ANBU protect the village from exceptional threats, conduct high-risk missions into enemy countries, and deal with extremely strong (S-Rank) ninja. They are also responsible for carrying out assassinations and missions requiring specially trained ninja."
I was thinking since an ANBU is a protector of their village and also perform special assasinations, then how about we make them do just that. Instead of battles in the Forest, an ANBU can focus on hunting down those of an Evil alignment.
Through PvP fights, if you as an ANBU decide to attack someone that is Evil, then you have protected the Village from a known Trouble Maker and Exceptional threat.
Your Superiors at ANBU take notice of your success and give you a certain Reward or Promotion. I have not worked out the exact awards one might recieve, but instead of collecting souls, you will recieve Merit.
You basically cash in your Merits by talking to your Superiors and they will either tell you that you should stop slacking off and get the work done or they will offer you a Raise/Promotion.
I know there is a major flaw in this and that is the fact that not everyone can really PvP against another because their rank is perhaps too high, but this is all I could really think of and if Gyu can perhaps fix what I've said then you will hopefully give this ANBU idea a shot since I've tried to make it different like you said