Did you use manual or auto in sport mode? I tried both and was much faster in auto. AutoX keeps you pretty busy versus an actual road course so it makes sense to keep all of your focus on the steering and throttle input. The car does a great job of shifting in Auto/Sport when you are actually using it for Sport.
I also use left foot braking when I run. Allows me to trail brake into corners better, as well as brake boost in corners where gearing is funny.
Tip: If you are using Auto and you accidentally hit a paddle, it will put you back into Manual. Just reach over to the stick, throw it into manual and back real quick and it will put you back in Auto mode.
Looks like you had a blast! You got the bug now, so be sure to keep us updated on what you learn and your experiences.