Get a removable front plate bracket from Woodhouse, put it on and mount the plate. Take a picture of it. Get the car inspected as scheduled. Take the picture to court with you. Plead no contest to both charges. Explain to the judge you don't drive the car everyday, and that you had an appointment set up for the day after you got the ticket. Show him the inspection receipt. Take along something that proves you just got the car. The dealer didn't mount your plate bracket; after the ticket, you mounted it yourself and here's a picture to show it's mounted now. If you're lucky, the judge might dismiss one or both charges. Of course, you still pay court fees -- they get their money. As someone else said, there are no points charged for the plate violation, so even if you have to pay it's no biggie. Optionally, remind the judge it's a brand new car, so it's not like you were driving around in an unsafe vehicle.
I got nailed in Virginia a couple of years ago for speeding (first ticket in 18 years), and the State Cop also wrote me up for failure to display a front plate. I made a court appearance, plead no contest and was allowed to take a one-day driving safety course and the ticket was dismissed. If I had done what I've suggested to you for the plate violation, he would have dismissed that charge too. As it was, I paid the $25 fine and court costs -- no points.
If you're lucky, the judge will realize the cop was/is an A-hole, and might cut you a break.