Bi-directional potentiometers
There IS a potentiometer that does something very similar to what you want.
It is called a balance potentiometer.

Basically, it's used for exactly what it sounds like - Handling Left/Right balance in an audio system. It's effectively two potentiometers back to back, with unusual tapers.
When the pot is centered, both halves are close to zero ohms. When you turn it one way, the resistance on one half increases, when you turn it the other, the other half's resistance increases.



Bourns makes at least one here, but it is carbon composition, so not the highest quality..

I would imagine there are other manufacturers, but it is not a common item.

You are probably far better off using a plain old linear taper pot, and a MCU to handle the forward/reverse/dead-zone translation. Plus, that way you get adjustable acceleration curves.