Okay, so the theory is
Walk Away = Owl
Noncombat Result from Choice Encounters = Raven
Combat Result from Choice Encounters = Hawk
That seems to fit with results and thematically with the bird species and the feathered cloak +choice encounter effect.
So let's keep track of choice encounter choices (beginning immediately after you get a feather, so we don't have prior choices working in there) and we should see if there's a set # of choice encounter results of a certain type you need, or something else. I recommend the non-etheric Midgard Laboratory in disguise, since it's entirely choice encounters.
Once we get that worked out, we can determine whether the counter for feather getting resets if you unequip the cloak, or with rollover. (Who knows, maybe it even gets progressively harder each day to get feathers — let's divide the data for an individual by rollover).
I presume it's only the ultimate result of the choice encounter that matters, in cases where you can have a prolonged conversation with someone. But who knows, the laboratory would also be a good place to check if there are even more feathers for choices that result in items, credits, or conversation even.