This is my opinion, so I apologize in advance if it offends anyone.
I have a 10 year old pit bull. I cannot imagine giving him up to a shelter or putting him to sleep, not for anything. I did, however, leave him with my folks when I moved, but not for any reason other than my mom needed him more than I do. The only reason Diesel would ever be put down is if it were for health reasons or if he hurt someone, and giving him to a shelter would NEVER, EVER be an option. Seek professional help. PM Jamie Dog Trainer, she is a member here and she is the best person I could think of to help you. Take him to a trainer. SOMETHING... there has to be a reason, a correctable reason, for his behavior. Take him to a vet, have his labwork done, but please don't give up on him. Pits have a bad enough rap as it is, and a pit that does not show aggression towards other animals, especially small prey animals, such a chickens, is an asset to the breed as a whole. There are members on here who would just as soon shoot Cletus as look at him, simply because he is a pit, but obviously in the past 9 years you have done something right, because other than the recent destructive behaviors you have been dealing with, he sounds like a model dog.
Ok, rant over, but seriously, PM Jamie Dog Trainer, and if she can't help you, get ahold of a trainer or ask your vet for help. He is a beautiful boy... I can understand totally where rebuilding things over and over and over would get real old, real fast, but there has to be something that can be done.
ETA: I don't like your third option at all, and for those of you who voted, think about this...
There are tons of conflicts and wars going on across the globe right now, I guess that means the world could end tomorrow. Perhaps we should all quit our jobs, school, etc tonight so we can spend the last remaining hours with our families. Imagine what the world would be like if we lived our lives based on "what if's" or "could be's"