What exactly is the problem? It's common for a FWD car to drag its arse with the handbrake on, especially with those new-fangled electric handbrakes that have a mind of their own

Instead of low grip rear, high grip front, try the other way around - i.e. CH front, RS rear. That's assuming you're trying to do a stationary burn out?
In every GT game I can remember, the handbrake / rev thing has never worked on FWD cars - you need to stop and press and hold the normal footbrake instead, and then rev.
The handbrake method only works on RWD / 4WD cars because the game automatically puts the clutch in for you