Ok, making progress.
First thing I found (and my first mistake) was thinking that the wireframe curves would be sufficient for defining the curvature was wrong.
Second, I found that the surfaces (even if the part won't actually have those physical surfaces) adjacent to the smooth (G2) surfaces must be defined. In my case, these were the two cylindrical surfaces that represent the final smooth airflow direction and the 'rim' type surfaces perpendicular to the airflow.
With those surfaces, I could then go and define the end points of my styles curves to be Continous.
Then I could go and make connections between the style surfaces and my reference continuos surfaces by selecting the broken line indicators.
If more than one surface was possible, then you would get a prompt like this (asking if the red surface was the correct surface to connect to).
Once those connections were made, then I could set those connections to be surface continous (they defaulted to tangent).
Still have some investigation to do and cleanup, but this looks like a solid solution.
