I'm currently playing Screamer using a keyboard controller, and always go for manual transmission. But I can't see any way to control the car under braking. It's like the driver has mixed up in his own mind the brake pedal and the handbrake.

Is there anything I can do to get some stability under braking? It's not a game breaker, but it'd certainly be nice. :)

No, because that's the game mechanic. Like in Ridge Racer, you have to break quick to drift through the courses.

To me best way is to quickly gear down then gear up when you enter a curve, you don't loose time and you gain a lot of grip and acceleration. The IA can't beat in anyway with this.