The penalty is what it is. You can't be convicted and start negotiating some sort of deal. If you are convicted of going through a stop sign, you are going to get 3 points no matter what. You don't get the luxury of having a trial and then bargaining some sort of smaller charge. You can't have your cake and eat it too. If the charge has a minimum and maximum fine payment, there will be a decision made there. If you need more time to pay off your bill, you can ask for the help. They'll put you on a 30, 60, 90 day plan or whatever.
If you wish to make a plea bargain before your trial in return for your guilt, you can do that. You'll have no trial and you'll plead guilty to the next charge lower in the food chain if that's made available to you. They will have to find a charge to bump you down to. They can not simply just remove points. Points are added later by the MTO automatically depending on your charge. If they offer you a smaller charge, your points would be calculated based on the new charge. If it's zero, then you'll have zero points.
Also, why are you concerned so much with the points? Do you happen to have additional points on your abstract?