Not wanting to use a op-amp/etc, I starting to think of ways to get this function with low cost and simple in mind.

Diodes have curves and are low cost, playing around a bit I came up with this circuit.
R1 + R2 = 5K steering pot (split for the simulator operation)
D1 & D2 = Curve function (mostly)
R3 = zero Ω is linear, higher values flattens the center steering
R4 & R5 = lower Ω is wider center width, higher Ω is shorter center width

Note: 1. silicon diodes seem to give better results over schottky diodes.
2. if your steering pot is not 5K, adjust values accordingly.
3. You dont necessarily need the diodes, short R3 and play with R4/R5.

To figure out what values to use, I entered it in LTspice and played with some values.
https://youtu.be/eRZ-gffFQeE

Of course a pot for R3 and a dual gang pot for R4/R5 would be optimum on the fly tuning (during driving) to your setup.