Thanks, those details help in understanding. If I’ve got it right, you want to be able to take 2D curves and map them back to the SubD. I’d do this with Squish and SquishBack on a mesh created from the SubD as shown in this video and file I made.
Upper-Squish-Pattern.3dm (2.5 MB)
There are a few things I’d point out that will help in copying this workflow that I don’t show in the video. First, separate your SubD into parts using ExtractSrf and Join as needed. Crease the SubD verts that are on the ‘corners’ of the open edgeloops before the next step so that the edges meet up fully. Then use the Mesh command and the Simple Slider to make a mesh from the SubD halves. Join the SubD back together and run Squish on the meshes you made not splitting at the seams. You could also use Pull as a final step to make sure the SquishBack curves are exactly on the SubD.
I also didn’t show it but you could Squish some curves with the 3D mesh too if needed.
I hope this helps!