My end product is this. A directly driven rack and pinion connected to the sliding potentiometer. It all fits very well, more than enough space, but the unit can be a lot more compact.

I already confessed to my little screw up, but luckily, the misalignment was about 1 to 1.5 gears and does not impact the performance very much it seems. The part I messed up is this one :

See how the Lego bushing fits into the original axle guide for the rotary potentiometer. It is the back plane of this part that receives the rack and pinion assembly. Without the universal joint and the stiffness of the bolted assembly, the whole experience is a lot more controlled and reactive. Of course if you want and the game allows it, you can make it as smoochy as you like.

In the end, this is a very effective and simple fix. You can fabricate this from about any material you have laying around I think. The Lego is nice for finding tolerances and trying new configurations and gear ratios, but the simplest method would be a wood or metal enclosure for the potentiometer and the sliding rack, bolted to this part which has the right ratio gear at the end of the shaft.

If you loosely use the configuration I have, the results should match up. This is a Lego pitch rack with a 40toothed gear attacked to a 60mm travel sliding potentiometer.

I have now played quite a few aggressive rounds of Dirt 3 and it still holds up!