TheMimizu: It seems to me that the game has unusually tight deadzones for the controller, exposing even minor defect of the controller's stick that won't affect any other game (it's the only game I have problems with).
After a while of searching and experimenting I've found the solution. Download a tool called x360ce. It's an XBox controller emulator, but you can use it to tweak some parameters in real XBox controller. Copy the x360ce_x64.exe file to game's bin/x64 folder. Rename the original xinput1_3.dll (i added "_original" suffix). Now turn on the tool. Set up deadzones in the card related to the faulty thumb. In my case giving the Left Thumb 12% deadzones in X and Y axis did the job. Also, go to "Advanced" and turn OFF "Pass Through" if it's turned on and turn ON "Force Feedback Pass Through". Push "Save", close the program and play the game.
Thanks man!!! It feels much more responsive, specially on tight turns or when I want to start walking really slow... Silky smooth movement...