The problem is you went to the DMV and not the court, as I bet you understand quite well now. You did not show the court that you paid the registration.
It is true that the fine for driving without registration is substantial. It is legal. I think you are out of options at this point.
However, I would talk to Andrew Roberts, an expert in traffic matters. You can do an attorney search on Avvo and ask him. He is the best.
Get an attorney to deal with this. There is a failure to appear on your license as you never went to court. This has to be lifted and the matter set for trial. Your license can be suspended if you wait to long.
ANDREW ROBERTS CRIMINAL AND TRAFFIC TICKET DEFENSE ATTORNEY