I used a DFGT to Gold this event but I will share the approach I used.
1) I couldn't react fast enough to drive competitively when I tried at first. My reactions were too late. I quit trying.
2) When I qualified for the Redbull Challenge I started to try it and was having the same problem only worse.
3) I had been driving manual transmission and switched to automatic on Redbull which helped considerably because now I had only to concentrate on braking, turn in and acceleration. I worked on Redbull (I still haven't even bronzed on it) and my times were getting better and I was beginning to "keep up" with my driving.
4) I went back to the FGT Challenge and all of a sudden the race was slowed down and I could start winning the races. I got gold in the Challenge by winning all the races except Cote and Sazuka.
I really like the Sazuka track and find it very challenging with the FGT. I can beat the best AI cars on a lap or two basis but they rarely make big mistakes and I found it very difficult to drive at winning lap times at Sazuka for 20 laps without making a big mistake (a spin out, or a badly over shot corner). I kept working on Sazuka until I finally got gold in it.
I may go back to Cote and try it but it is a very difficult track to win on unless you get to the lead very early. It isn't all that easy to do...
So for me switching to automatic and driving the Redbull Challenge were the secret to getting gold in the FGT Challenge.