I don't know what to do at this point.?

Two months ago our neighbor found and english bulldog/american bulldog mix. He was wondering around a car lot underweight and scared. He didn't want another dog and we decided to take him in. At first he didn't get along with the female dogs I had but he came around. He's not affectionate with them even though they are with him. My male Mastiff he hates. I tried introducing them multiple times leashed and in the process I got bit. He is not neutered and I know part of the aggression is from that. I have tried every training method I could read about with him but, I still can't have him around my male Mastiff (which is not fair to him). He has even shown aggression towards us if we try and move him off the bed he'll growl. Today our atoo broke out of his cage. This happens occasionally, atoos are escape artists. Our other dogs, when this happens, do nothing they just continue about there way. He was on the bird before I could even get to them. The bird did get a minor cut just under his eye but other than that he is ok. At this point, I feel I've exhausted every effort with this dog. I have had dogs all my life and have never dealt with this type of aggression. I also got all my dogs as puppies and they knew from the getgo that was not allowed. I feel there is no hope for this dog. Maybe someone more experienced could help him but I can no longer keep him he hasn't benefited from any of the training I've tried to give him. I don't want to take him to the humane society the thought of just throwing him to his death bothers me. But what can I do? I can't keep him in my house disrupting my other dogs, my bird, and our lives. I'm just really torn right now. I love dogs. I've had dogs all my adult life and they were all amazing. The thought of just giving up on one and sending him to his end is to hard for me to imagine. By my vets estimate he is two years old so I'm not even sure how much neutering him would help at this point. Any advice, info, anyone could give I would greatly appreciate. He's sweet and happy with us most of the time , knows the basic commands and does them when asked but when he gets that attitude so far nothing I have tried has helped it in a way I feel it should of by now.