What you describe is effectively a servo.
When you drive, you don't know the position of the rack (some cars have mechanical or electronic systems for adjusting the applied movement depending upon speed and are not 1:1), you turn the wheel to achieve the required radius, as I said, you are part of the feedback system, all you are doing is turning the wheel remotely.
If an RC car travelling at ridiculously high scale speeds is able to cope using an RC servo (using a single turn pot), why can't you just scale it up?
Turning the wheel 15deg on a RC car or a real one, only really differers in the scale of power required.
They have done this a bunch of times on mythbusters, so it can't be too hard. The video is probablyon youtube.
The whole thing could be done with potentiometers. Multiturn pots at each end. What you would be making is just a bigger version of something similar to a standard hobby servo. Basically - at the steering wheel end you would be "creating" a refernce voltage that you would then compare to the voltage present at the gearbox end. and then itf the voltage is higher or lowere you use that to decide the direction and speed to turn the motor on the gearbox. The difference between the 2 is referred to as the "error voltage" This can be done with linear circuits or Analog to Digital circuits.Using a couple of potentiometers is probably going to be much simpler than using encoders, as absolute encoders would be needed and they get expensive. A good multiturn pot would give good, repeatable feed back.