On relatively flat water like that, and in view of its extreme clarity and the bright sunlight, I'd be concerned about the disturbance that might be caused by the line.
To this end I'd certainly avoid the double spey or any of the other casts that require two moves. Being strongly left handed I instinctively favour the LH snake roll over the RH single spey, though the RH single makes less disturbance. The RH single spey also places whatever disturbance there is further away from the fish, and thus would be the better spey cast in these circumstances. Obviously wind direction (if any) comes into the equation, though.
But if I had adequate room behind, I'd be inclined to go for an overhead cast rather than any of the spey casts, wading somewhat deeper if necessary (which might improve the angle of presentation, too). An overhead cast would enable me to use a lighter line on the same rod, giving me a far more subtle and stealthy presentation than the rest of you with your fat spey lines!
I don't know about fly patterns for over there, but with clear water and bright sun I'd go for something small and not too bright. But I'd prefer to wait until the sun was off the water before starting to fish.