Wow!!!
Your experience parallels mine, exactly but for the near disaster at the end. I was invited by a client to attend a race in Charlotte several years ago as their CEO sponsored a team. Like you, I had access, full hearing protection and got to stand behind the lines for the start. They were shooting 4 up at this time.
Nothing can prepare you for this.
I'm fairly certain I was having heart palpitations from the vibrations the cars caused. I experienced everything you described. It was nerve wracking in the extreme. I've never felt unsafe at any race track until this time. It gave me the heebie-jeebies the entire time I was back there. I lasted 4 races then decided to go to the finish line and "enjoy" the race. Nope. Not enjoyable. A car passing by at 330 MPH was not fun for me.
Great and unique experience...but I'll never do it again!!
Have you been back since then?