The parking brake is a sudden death on or off mechanism
You are supposed to stop the machine using the transmission control then hit the brake
And when you go you release the brake then move the motion control lever
If it leaps forward when you let the brake off then the motion control lever is not in the neutral position so needs more adjustment
The general rule is to adjust it till you just barely move backwards with the lever in the neutral position then adjust slightly forward till the mower just stops
Check all of your linkages in the motion control system
good chance you will find some with badly flogged oval holes thus introducing a lot of slop into the controls .
Other problem is a badly adjusted brake balance
The rod that connects the clutch & brake together has an adjustment on it
What is supposed to happen is just as the belt gets tight enough to make the belt spin the brake should fully release
If the brake releases too late then you have a one foot on the brake & the other on the accelerator situation