Another site, which you are aware of, has a certain section where a select group of members post but they all have different aliases for that section so they don't know who's who. So surely you could make a section where all members that post are renamed "Anonymous" and there's no way of telling who's who (Besides maybe Administrators having access to check each posts' IP)
I think many people could be worried about giving a staff member negative feedback. Feedback is going to affect a staff member's opinion on the poster no matter what I feel like. It shouldn't effect the way they work, and it may not, but it will effect the way they think for sure. I disagree with the second part completely though! I'm not condemning biases completely, because everyone (including myself) is going to have them. Whether they want to or not. Some on a smaller scale than others, but it's always going to be there