Stop Braking Later and Praying!
The last way you are going to find speed in racing is by braking later. The last way.
To find laptimes, first you need to get the lines and the EXITs right. It's maximizing the minimum speed and exit speeds first that you will get the biggest chunks of laptime performance. And only then, you start braking later and later at the expense of having the higher risk of making bigger mistakes. In real life racing, that's a very common mistake: A lot of people try to just brake later and pray, brake later and pray, brake later and pray, no! Brake later only if you realize that everything else is perfect already. Don't overdrive the entries, get good exits. Then, don't over drive the corner, but get even better exits, and with this process, you might be surprised with your laptime improvement already.