It's a strange situation with my neighbours. They left a rude sticky note on my door when I was at a school assembly saying the dog was howling - again! At that point I had no idea he was howling at all, as he'd never done it before we lost Oldgirl.
Then when I went to speak to them and explain our old dog had died and the younger one was distraught, but we were doing an intensive separation anxiety programme they were very nice about it and said not to worry, chatted about their brother's gundogs etc. I spent a fortune on treat dispensing toys and kongs, spent hours going in and out, desensitising him to leaving signals, walking him for 3 hours or more a day etc and he made slow progress at first, but then seemed to suddenly improve for no apparent reason.
I explained to them we had decided not to get another dog when we lost Oldgirl, but that all the behaviourists we'd spoken to had suggested that in Lurcherboy's case getting another dog was probably going to be the only thing that worked long-term. I told them I didn't intend to get another dog until we'd come far enough with the SA programme first, but if they saw us with another dog, not to think we were being irresponsible, because it had been recommended by both general behaviourists and breed specialists.
When I had to go to another unavoidable school event I put him in my bedroom, which is on the other side of the house to theirs and put a note through the door apologising if he disturbed them and explaining I'd only be an hour at most. They said they didn't hear him at all when he was in there, but it's not really an option, as there's barely room for a crate and after doing it a couple of times he was wise to the fact that being allowed upstairs meant I was about to leave him. 
To be honest, I think they'd be ok-ish, as we're only talking about him being left for about 2 hours once a week, perhaps twice some weeks, but they are very hard to read and I am so anxious about it myself that I can't bring myself to try. (They are both retired, with no pets or children, so not ideal for living next to a noisy dog.)
We don't bump into them on the drive, despite being attached, as there's a huge leylandi hedge between us and they never answer their front door, so it's kind of hard to catch them for a chat about the new pup, although I did introduce them to him when we first brought him home and they know he's a rescue.
Dh has learned all his dog-knowledge from me, so can't really come up with anything new. I think he'd probably just bite the bullet, leave him and see how it goes - it's me and my anxiety that's the problem really.
at your poor resigned pooch. My two have been playing Gozilla and Godzuki to dd's train track and village this evening. She was cross at first but then saw the funny side when Pip kept derailing the freight train with a look of sheer delight! 