You can always do some sort of iterative approach. You align all three on one plane and then you move them around. But honestly, from what I see at the pictures, its very likely that there is simply no solution. So I’m not sure if its worth all the effort. I would rather make it quite compact, and live with the cutoff (?). Do you script?
Furthermore, although you apply some sort of minimal surface optimisation you can still reapproximate this shape with very few cps. The less you take the higher the chance the surface is smooth. Minimal surfaces are surfaces where the summation of both principal curvatures equals 0 (indirectly mean curvature == 0). Using the mean curvature analysis you can even model such a shape without any optimisation algorithm because the analysis tells you where you diverge. Since you are using Nurbs you cannot reach perfect 0 mean curvature, which means you will have certain deviation anyway. It just makes sense to reduce this heavy data for many reasons. You can even modify the shape for production purposes (if this is a degree of freedom you still have…), and still having a minimal surface.