It shouldn't be too hard to run a license plate light off the trailer light connector block. Get a magnetic license plate frame like car dealers use, mount the light to it, and you're down the road. Assuming your rack is steel, anyway, which hitch-mounted racks normally are?

If I understand you right anyway ... the ticket was for an equipment violation, not for failure to display plates, and it's one of those things that you just have to go to court and prove you fixed it?