I am not a fan of expo rates because they tend to create snap oversteer issues if the expo rate is too aggressive, what you are describing is the same problem in reverse having a steering lag on return to center which is exactly what expo was designed to do.

Consider using the steering speed setting instead which will keep the full range of steering input linear and make the car easier to drive at the same time being a win-win for what you want.

Another thing to slow down servo speed (besides installing a slower servo) is to reduce your BEC voltage on the ESC if possible. In contrast, I often max out the BEC to 8.4V just to get my servos to turn a little faster