please dont shoot whatever you have, why dont you have a look at a 300E W124 mercedes benz - it will stop so fiercely that you will have a headache, It has got 4 regular sized disc brakes (same as corolla). The reason it stops so quick is suspension design, the rear suspension has anti dive, antilift and anti squat setup, meaning it does not induce lift on braking. And the wheels provide traction. The ABS does not engage very often unless on ice.
The corolla brakes are ok to work with, its the lift the car faces while driving that causes stupidity. hard brakign causes rear lift and sway. adding drums will not favour you. They will be the same.
in the US all corollas from CE to S have the 1ZZFE engine with front disc and rear drums, ABS standard, they stop reasonably well.