OP I don't the answer really, I still suffer with DD1. I like the crying method (obviously not to the point of hysterics), but my neighbours bang on the wall (when DD1 wakes & refuses to sleep after midnight). This scares her, so she cries more frantically.
I've spent many a night (with disastrous consequences) trying to appease DD1, and staying awake ALL night, so the neighbours don't get pissy. It resulted in me slipping on the stairs, when heavily pregnant last year, and having a bleed, although DD2 was seemingly OK - she died just over a week later. I have no idea if the slip contributed to it (probably not), but the fact remains - I was so bloody scared of my neighbours that I was exhausted (DD1 was up from 2am - 6am some nights).
DD1 can still be a pain at night, but if I leave her she does settle (obviously I check her, soothe her, change nappy etc first), but if she's fine, I want her to go back to sleep before she wakes properly (which she does if I stay with her).
To be honest though - my neighbours can be funny anyway - during school hols/weekends - they are up till 3am, banging, so now I don't care if DD1 wakes as much.
In your situation it's hard. It's not fair on you obviously, but I guess it's up to them how to parent. Sorry no use :(