I have a similar problem. My throttle only works when I am turning the wheel. Try turning the wheel back and forth while using the gas pedal and see if that is the problem. If it is then you have the same problem as me.
I figured out what my problem was. Analyzeforspeed showed my throttle as 80% instead of 100% on the straight. I recalibrated my pedals and all is well now.
In your replay I noticed you have a half tank of gas. Try using just enough gas to make it around a couple laps. The decrease in weight may decrease your times. Its worth a shot.
I'd be interested in joining your driving school. You said you are considering have classes for demo users as well. Have you decided yet?
Also, you said all communication is through teamspeak. What if I don't have a microphone?
ok I am in the exact same boat as you my friend. I spent the last week completly focusing on the WR replays and observing other guys online who get in the 1:23 - 1:24 range. I see everything they do but I can't get my car to do it. As you mentioned they corner like 10mph faster than me and I've tried it and its just not possible for me. I am at the point now where I get in the 1:29's and 1:30's but if I try to pushing the car any faster I will spin out.
I'm gonna go check out analyzeforspeed and I'll let you know if I figure anything out.