I've been told there is no reciprocity between DC and Virginia on traffic infractions - which no doubt accounts for all the DC drivers acting like idiots on the Beltway as they approach the border or the Wilson Bridge. If this is true, then the solution is just visit DMV for new tags (tell the clerk you feel your current plate contains "unlucky numbers" and you need a new set) and avoid driving in the Peoples' Republic of DC. Even if you do enter the district, they'll be looking for a car with your old plates so street parking and finding your car booted isn't a concern. You'll start getting letters from a DC collection agency with a fine that's doubled, but that can best be dealt with as a credit reporting problem.
Yes, I have a problem with DC government and their crackhead leaders...
The chances of the judge reducing the fine are nil. You're dealing with a totalitarian state that uses red light cameras as a major source of revenue and also wants to impose a commuter tax on residents of VA and MD just because they can't seem to manage their own budget. They'll squeeze every dime out of non-residents and pass the funds on to some street thugs as part of a "social program" or maybe pay for Marion (Mayor-for-Life) Barry's next trip to drug rehab.