Oh blue :-(
I am going to second the idea of talking to a behaviouralist and getting some help. It may mean going back a few steps and relearning behaviour: will you be able to leave him for shorter periods for a little while or have your parents visit a little more often for a few weeks?
As a remainder: 10 days ago I had a pup who barked at anything and everything on lead: he was right at the end of the lead, barking like a mad dog. I was definitely in 'back to the breeder' space - I just couldn't see how we could get through it. I cried and cried. A week later, and it's like having a different dog.
I have had to take a breath, and not try and rush things: so pup is great in a single park, so it's now about moving that behaviour across to some other places now (first new place - two visits down and only one little bark - hurray!) - I would definitely have tried to move too fast if she hadn't been there to guide me. I'm not walking him on pavements yet, and that's hard for me having read so much 'socialise, socialise, socialise' stuff. But I'm confident that we have a plan and that makes it manageable. I'm sure you can get to the same space with bluepup. He sounds very loved :-)