If you delay payments to them for similar reason, you'll probably get an invitation to a court. How come you can't complain to the court about such a behavior?
That said the fastest way to a resolution is often exactly this. Either get a lawyer to send a letter saying you're gonna file in court, or just file for arbitration yourself.
If money on that scale is at stake, this is a comparatively cheap way to make sure a real human looks at the problem.