As the previous posts have said, the pushrod should be attached at the outer-most hole on the tiller arm. Also you should probably move the connection at the servo end to the inner-most hole on the servo arm. This also will reduce the amount of movement for the nose wheel. As said above, the wheel only needs to move 10 or 15 degrees right and left from straight ahead.

But it sounds to me that your main problem may be that the nose wheel pushrod is flexing when the model is moving and the wheel is under load. The manufacturers typically give you a very thin, flexible pushrod. This can be remedied by making a support from a piece of 1/4" balsa wood and gluing it between the plastic pushrod sleeve and the inside fuselage wall close to the servo end. Be sure not to glue the metal pushrod, but just the outer plastic sleeve. That should keep it from bowing back and forth.