While I'm sure some lurking PETA member will burst in and have me hanged for saying this:
I was in a very similar situation. In our case the neighbors had two large dogs (as did we, white german shepards). They lost both of their dogs in quick succession (about 6 months), and after that suddenly every bark out of our dogs was a problem (honestly, their dogs had barked much more than ours ever did).
That said, we researched it, bit the bullet, and found a vet to debark our two dogs. They were in the vet hospital for one day, their personalities did not change *one bit*, they just didn't make nearly as much noise as they used to when the barked. If giving your dog up isn't an option (and for most people it wouldn't be), I think you should at least look into it.
Ironically shortly after we did this the neighbors who complained moved (but at least we know we don't have to worry about upsetting anyone else).
Bill