I've been remapping the buttons with my Logitech F310, Problem is the game isn't registering the top button's (LT, LB, RB & RT)

so if i want to pull out the gun with the Y button and shoot with the RB button, RB isn't being detected by the game.

I know this isn't exactly a fix (and I am also quite late), but do you know the program JoyToKey?

You can assign keys to be emulated keystrokes on the keyboard, and you can rebind the controller with the keyboard settings. That's how I always play In Cold Blood (and a few other old games), anyway.