Many teams have used squaring the input to give better low speed response to the sticks. May try and see if that feels right to the driver.
If using xbox controllers there are buttons on the sticks, so you can use those buttons to give finer control, and square the input.
Code:
X X^2
0 0
0.0625 0.00390625
0.125 0.015625
0.1875 0.03515625
0.25 0.0625
0.3125 0.09765625
0.375 0.140625
0.4375 0.19140625
0.5 0.25
0.5625 0.31640625
0.625 0.390625
0.6875 0.47265625
0.75 0.5625
0.8125 0.66015625
0.875 0.765625
0.9375 0.87890625
1 1