Find a reputable calibrated noise meter that has serial output and connect it to a datalogger. Find an expert
witness who can witness the use of the system, and the actual readings being observed, and is willing to
answer questions in court about the measurements and their relevance to the legal case - anyone capable of
claiming 85dB is 55dB is also capable of pulling a few sneaky tricks so be ready. They certainly would trash
any claims based on home-brew equipment.
I suspect the best course of action is to employ a professional company whose business and reputation is
with noise management - they might see an opportunity to get work from the offender in fixing the problem
once the spectre of a successful prosecution is raised.