About 15 years ago,I had same problem,which(to cut similar crap you are experiencing) I resolved by engaging Municipality(was something about by-laws dept.) who send official and I paid R.500 for the authorized Engineer contractor(from their list of the Service providers).They measured normal noise comming out of my place and findings was in compliance with a Municipality by-laws regarding noise polution.
It was long ago,but I beleive that didn't changed in principle,than you can avoid humiliating yourself with a asshole-next-door and crooked lawyers.Hope it will give you some direction for the resolution of your problem.Regards,Trenk