I apologize. I confuse your build with somebody else's.
Anyways- I have had to put a lot of thought into it myself- one possible solution is a system of linkages that would sorta mimic a real rod. The steering column itself would only be a few inches long, enough to protrude through the dashboard. Just on the inside of the dashboard is the pitman arm. The pitman arm points straight to the right. A few inches below that, is a shaft that runs horizontally, the entire width of the body (this shaft is behind the dash, and therefore not visible. The pitman arm is connected to this shaft via a short rod, and an arm on the shaft which points straight forward. On the right hand side, the shaft rests on a bearing, and does not protrude through the body. On the left side, it passes through a bearing, through the body, and features a downward-pointing arm OUTSIDE the body. From that arm, a drag link runs towards the front of the kart, connecting to a steering arm on the left-hand spindle. This arm would come off the spindle, parallel to the front axle (pointing straight right). Of course, the two spindles would be tied together with a standard drag link and steering arms.
So- When you turn the steering wheel, the pitman arm moves up and down. That in turn moves the first rod up and down, causing the horizontal shaft to rotate backwards and forwards.
This causes the arm outside the body to swing back and forth, moving the drag link back and forth. That, in turn, causes the steering arm to swing the LHS spindle left and right.