#7. "RE: Company Unknown 703-434-9721" In response to Reply # 6
There is a national number database with access restricted to law enforcement. I forgot the name of the organization. However, even that probably won't help much for cell phone and voicemail numbers. For those, it probably only gives the carrier responsible for the number.
Your city attorney (or district attorney) would be the who could advise on what kind of sting would hold up in court. It heavily depends on local ordinances and state laws. Stings have worked for some cases in Texas.
Finding someone hanging the signs would be ideal but is tought to do. Maybe you can find who is printing the signs. That might lead to to is hanging them or paying for them.