This is an interesting question since I know of no specific time limit for filing the ticket. However, I suggest that there may be a speedy trial issue since its a Violation and they must be ready to go to trial within on a Misdemeanor within 90 days of being charged and I believe normally within 30 days of a Violation. In this case, since it is not a criminal matter, the statute (CPL 30.30) may not apply.
I suggest you hire a local experienced lawyer and discuss whether to have him/her move for Dismissal IN WRITING ( a Motion to dismiss must be in writing to be effective) so that the court must make a decision in writing.
30 DAYS TO LODGE WITH D.A AND 90 DAYS HENCE TO FILE CHARGES IN THE STATE OF NEW YORK(FOR WHAT YOU DESCRIBED.) I DO NOT UNDERSTAND THE OTHER COUNSEL'S RESPONSE OR I DO NOT UNDERSTAND YOUR QUESTION. PROBABLY THE FORMER.