Hi Steve,

I have attached my approach based on your example.
Yust hide the solid and switch on the controlpoints with the Show pts command.

What i did is projected the blue lines on the shape.
Then trimmed the curves at the border and turned on the controlpoints
With Line/both sides command(see green lines)snapping on the endpoint of the mastercurve(orange) and the nearest controlpoint.
I switched on the controlpoints of the cyan colored curves and snapped the nearest controlpoint on the green lines.
At last i used Sweep/two curves.

Ps. You can play with the rebuild command(R shortcut key) to add or reduce control points.