The primary reason mower steering is sketchy at high speed is the narrow track width being narrower than the rear for a start. To add to this tip tempting configuration they function on a center pivot with no suspension resistance and generally in excess of 10" travel from level.
You want to stabilize it and deaden the sensetivity for speed you really only need to find a wider front beam that fits or make one, obviously this would entail longer tie rods, then add coil over shocks (something like motorcycle rear shocks) which would require adding some framing which would need to be tied together over the engine. Better spindles and wheel bearings would help too.
