Poor Dog - he's only doing what dogs do, to try to be part of the family he loves, who is now ignoring him.
With all of these issues he has, I wonder who you think is going to want to adopt him? Or are you just going to fail to mention his barking, jumping, shedding, etc? If you aren't upfront about all of his issues, you run the risk of his new family dumping him as well.
If you adopted him from a rescue (well, a reputable rescue), you probably signed an adoption contract that states if you ever have to give him up, you're required to contact the rescue first.
If you're determined to rehome your dog, that's where you should start - contact the rescue you adopted him from. They might take him back into their rescue.
If you adopt him out personally, you'll run a lot of adopters off if you're too aggressive with home checks and such. Many people turn to personal adoptions to avoid those kinds of things from the shelters/rescues.
Should you surrender him to any kind of shelter/rescue (including the one he was originally adopted from), be prepared to be blacklisted by ALL rescues in your area. Surrendering an animal typically gets you put on a "Do NOT adopt" list and most agencies in an area share that do not adopt list amongst themselves. They don't want to adopt a pet out to you, knowing you've been fickle towards non-human animals in the past.
I hope your dog finds a loving family, who will incorporate him into family life, and give him lots of love and attention.