Thats how i was thinking too. Then i took a different approach. Braking much earlier and using momentum to take me through the corners giving me a much higher cornering speed and better acceleration + grip.
I can keep up with the ghost of the top no 1 person in the world in the first section. Just after that he starts pulling away and i cant close the gap. More practice i guess.
here is a tip for some people that i get from riding a motorbike. When you downshift (gear down) under braking make sure you blip the throttle during the down shift to keep the revs up and the car more stable for turn in.