Pretty sure pleading guilty won't help you much. But my buddy got a pretty bad speeding ticket, and also a stop sign roll-through ticket in the same week.
He went to one of those ex-copper places. The one on Cawthra with the fake cop car parked outside it all the time? They pretty much guarantee your tickets will be dropped or the demerits removed (they just contact the cops who gave you the ticket and tell them not to show up to court or whatever).
That headache will be gone, but the bill will be significantly higher than the cost of your tickets combined. They also add in some BS about some community benefit donation/fee or something IIRC lol
Basically you're paying extra to avoid the insurance hike, but it's usually worth it. Sucks though.. sorry about the bad luck