You need a way to increase the deadzone. I've looked into this previously, but haven't really found a good way.

If I remember with gamepads you can:
- set the deadzone (the area where moving the analog stick results in no steering wheel movement)
- set how linear the steering moves (for example less sensitive around middle)

For "Smoothing out" the gamepad-input there is no option.
The analog-stick movement gets translated directly to movement of the virtual steering-wheel.
Same happens with mouse and normal FFB wheels too. In case of mouse/gamepad that produces unrealistic situation you described of instantly steering lock to lock and it is way too sensitive. (imo, some might get used to it) With wheel that is not a problem.
If the gamepad-input was smoothed or otherwise modified it would cause strange situations, like:
You have the physical controlls moved to "left lock" but the virtual wheel is still slowly rotating to catch up.

Analog steer smooth in misc for smoothing the steering. There is no way to fine tune deadzones, all you get is remove deadzones yes/no.

Wow, indeed. I always had that at 0.0 (wheel) and thought even the maximum settings would only smooth the input a tiny bit. Like for bit jerky wheels or so. But at higher values it seems to smooth quite strong.