Wondering how much my insurance may go up after moving violation

I live in NJ, and was recently traveling through NY for the holidays. I got a ticket for failing to vacate the right lane when there was an emergency vehicle pulled off on the side of the road.

Now, the ticket only has a maximum penalty of $243 for first offenses (up to the judge), and puts 2 points on my license for an out-of-state offense, but I found a law office that says they can get it reduced to a parking ticket for a flat fee of $750. And if they can't get the 2 points removed from my record, they have a full money-back guarantee.

So my question is, is my insurance likely to go up by more than $500 over the next several years? Just wondering if paying the $750 is more economical than paying the $243 + increased rates.

I currently pay about $110/month for my car insurance (from Progressive). I pay 6 months in advance.

Thank you all for reading and for your responses.