What I would do- I'd write about 100 page report for the section on the basis for appeal. I'd forget to sign it also, maybe even use your screen name, since it doesn't mean anything on that paper. I'd go to the appeal hearing with as many lawyers as I could find and waste many, many hours of their time. If your 100 page report is well written, you may tie them up for weeks. In the end, if they don't reverse the civil citation (most likely, since they don't get money if they reverse the citations), I'd simply not pay (I can afford to have a small mark on my credit report, since I don't need it). Make them earn their $50 or $100, even if it costs you more.
The main goal is to get it past their "administrative appeal" process and into the real courts on appeal. By having the 100 page report, you'll have plenty to appeal.
Good luck Darth, I really don't like those revenue enhancers masquerading as police these days. The last one who gave me a speeding ticket couldn't even tell East from West!
It is an improperly delivered summons though so you might be able to just ignore it until they come get you. I doubt that they can legally deny you an appeal for failing to respond to something delivered by regular mail. Now if it was delivered registered mail, you should just pay it.
BTW, the photograph clearly show the car entering the intersection (busy , no less) with a car waiting on you in the left turn lane and now car behind you. I think you should just pay it.