Road Rage Style Driving Controls For Hit & Run

I struggle to use the keyboard and mouse controls for Hit & Run so I use a joystick to make things easier.
Right now, I have the PC version set up with fully usable character controls however the car controls barely work and I keep crashing into stuff.
I also have the PS2 version running on the PCSX2 emulator and after some tweaks to the controller bindings, I managed to get a setup with usable steering and partially working breaks however the character controls are a mess and I don't want to change anything because it could mess up the car controls.

I'm trying to make the driving work the same as it is in Road Rage by changing the control bindings but all I do is make things worse.
Due to these issues, I'm always blowing up the car, running out of time, losing races, failing missions and have never been able to outrun the police during a Hit & Run sequence. I've also never been able to drive the entire Evergreen Terrace map without veering off the road and crashing in the process.

Is there anything I can do that will make gameplay easier? At the rate I'm going, I'll probably end up winning the lottery before I have a playable Hit & Run game.
For now, I'll just keep tweaking the bindings until I get something that works like the controls for Road Rage.

Why not start practicing mouse and keyboard since you already use a PC?