I think the game is simply hardcoded with a sensitivity curve and deadzone specific for the Dualshock 2 pressure buttons on a regular PS2. Some third-party controls aren't too great to use with PS2 GT games, too.
Patching that is possible I guess, but it would also require setting up some sort of calibration in the game.
Most people I know use the DualShock 4 for PS2 emulation. All you need is to write a mapping for the DS3, 4 and 5 to the DS2 curve and you can cover a big part of the users.