Hi There,
Reading through your requirements caught my attention as I have a solution in mind.
A few questions and comments though,
1) You have a total of 12 LED's that need brightness control. However, the Arduino UNO you have has 6 PWM pins only. That means only 6 LEDs can be controlled INDIVIDUALLY. However, individual control is not necessary, then we could combine a number of LED's on one PWM pin.
2) I suppose he car is only travelling in one direction from LED 1/7 going to LED 6/12 right?
By the way, I am an electronics engineer with 11 years experience working with microcontrollers, almost 4 years of those I've spent on Arduino related projects. (I've spent 5 years of those in Singapore :) )
thanks,
Christian