The 4-stroke gearbox 250 has been talked about for many years.
But no one took up the fight to get it approved. There is at least one company which has a conversion kit to set one up for a kart, likely that would be not too hard to find. Consult with the current Kart Committee members to see what it would take. I personally have thought it a good idea for a very long time.
The single drawback always mentioned is the expense of repairs should anything go wrong with the engine. Top ends of those motors are not easy like the 2-strokes.