I asked sitek about the orientation of the nozzle, and this is how they said it should be. The inner diameter is constant through the nozzle to about 5mm from exit end when it opens slightly.
The 'normal' way a kort works is to have the wider end in to the water flow, the prop, then a slightly reduced rear end..
This way it works almost like a jet engine.. the water entering the kort is 'pressurised' and then forced from the rear of the kort at a slightly higher pressure than the water surrounding the rear of the kort..
The 'outer' shape of the kort should be thicker at the fromt and tapered towards the rear..
Imagine the shape (in a cross section through the kort) to be almost like an aerofoil section, leading edge towards the water flow.
It sounds from your description Boatmadman as if the wider opening is at the rear of the kort?...