I managed to win 3 tickets in CA (over a period of about 9 years) using trial by written declaration. In fact one of them was using a very similar argument to OPs. It's a bunch of work as I painstakingly assembled my case with loads of supporting evidence but I think it's important to stand up for yourself.

Admittedly all 3 cases were dismissed because the officer didn't bother to write a response but TBWD is a lot cheaper than lawyering up and does sometimes work.