One possibililty you do not seem to have considered: in some residential areas the speed limits are set low as a traffic control device. Even though it is possible for you to cut your trip short by using this road, the plan is for the majority of the traffic to be on the main road. The people who live on that road do not want it used as a shortcut, especially by people who might endanger their children.
I'm certainly do not want to be argumentative, but I live on a street like the one on which you were speeding. Although originally intended to be only a residential street, a few highway expansions in the area have turned it into a helpful shortcut. A few years ago, a few of us got together and petitioned to have speed humps installed. The county required a speed study to confirm the level of traffic and the percentage of speeders. Then, 80% of the residents had to agree to the speed humps, and to a small increase in our property taxes to pay for them. They help a little, but there are certainly still commuters who would rather deal with the humps than travel on the highway.
As others have suggested, contact the prosecutor's office and see if they will help you out. Do not go to court without talking to someone beforehand. The judges usually to not appreciate someone appearing to argue a speeding ticket, especially when you admit you were speeding but find the law unfair. They could end up adding on court fees to your fine.