1. I have had a pigeon for about one year and I noticed that when she over-eats and sits on her eggs for 20 days, she tends to hold her poop longer (she is very smart bird and does not want to poop around her nest - her nest is in my bedroom). So, being a very smart bird, she flys to the feeder in the corner of the bedroom and poops from or near the "designated pooping area". Very smart bird. Makes it easy for me to clean up. But her poop stinks to heaven when she does not poop very often. That happens when I am not around and she cannot leave her nest (eggs). As soon as I come back from school - she knows it is my turn to sit on eggs - and she starts flying around and pooping all those huge chunks of poop she was holding when I was not around.
2. She likes "service": when there are no seeds in the dish she starts flying from the dish and onto my head, and back and forth. That is her signal she wants me to put seeds into her dish. But recently I noticed she just want attention: she has seeds, egg-shells, stones, water, greens, etc (everything that a bird needs) yet she would start flying back and forth onto my head and back to the dish. She just want me to show her that I pay attention and that give her things if she demands it. She is just verifying the communication system is working. She just wants attention and service. Social bird.
Conclusion: the stinky poop is most likely from overeating and from diminished movements of the bird (sedentary lifestile). I notice MY OWN poop starts smelling like hell when I overeat and skip one hour of sweat-drenching gym session.