The lawyer who did the original court application for us is Adam Kalish, http://www.kalishlawnyc.com/ He did very well in court, but I think it may depend on who the judge is. Ours appeared to have already made up her mind before we got there.
We got the Order from the judge to create the birth record. Vital Records would not fulfill it. Then the City appealed the case. They say it's against their rules (which it seems to be). But in the meantime the Consulate gave us citizenship based upon the judge's Order. They originally said that they required NYC to create a birth certificate for our GF since one never existed. I'm not even sure we needed to go to Court at all, wondering if the Consulate would have accepted the proof that there was no BC for him. We'll never know. But if you are considering this, that's why I recommend that you just get a Declaratory Judgment that your ancestor was born on such and such a date, etc. and not to ask for the birth record. That's what the Consulate accepted and the City would have no problem with that, as long as the judge approves it.
It also seems to depend on which clerk you have at the Italian Consulate. I had a Declaratory Judgment and was waiting for a Delayed Birth Certificate to be issued by the time I had my first appt., but the Consulate would not recognize my citizenship until I got the delayed Birth Certificate, which I had in hand by the time of my 2nd. appt.
It seemed to me that they gave us an intentionally hard time on our first appointment all the way around, did not take any of our papers. Then on the second visit, everything was different even before we presented the judge's Order. The guy that had been so negative before had what seemed to be a personality transformation. He invited us all in to sit together (which they wouldn't allow before) and just accepted what we had. Very, very different attitude from the moment we came in the door. I wish we had waited to go to Court until after the second appointment, but honestly don't know if we needed the Order or our GF's baptism record (which we didn't have the first time around) would have sufficed. I know others at other Consulates have made it through with that.