Well, I give up. I tried 3 or 4 more times without success. I had tossed the feathers onto a pile on my homestead that already had a couple from the same species, and maybe the game internally keeps track of which bird they each belonged to originally and I got unlucky? Either way, no thief turned himself in. I'm not sure what went wrong originally, but I couldn't seem to salvage it.
Appreciate the help nonetheless Palu!
Edit: Gave it one last try, actually went and searched the message logs to see if I had the right feathers (and I did), and what's more is that every feather of that bird that I own is actually from the quest grounds and weren't mixed with other feathers. So I do have the right feathers. I also tried using a village sauna this time around, instead of a fire on base rock. Either way, my efforts were in vain because no thief turned himself in either. Oh well!