Simplifying reducing radius of mesh/brep curvature around EDGES only

To give some context I am building this to (separately) input hundreds of meshes varied in detailed form - these are equally scaled sections from a larger parent model which all needs to have individual layered waffles.

I am getting messy and missing contours from the initial raw mesh input being too ‘complicated’ and the contours trying to replicate its form too accurately. The mesh tightly curves in on itself at the inner and outeredge. Inner and outer edges being where this causes the most issue for the contours I think.
I start with a raw mesh from a 3D scan then quad mesh it then subD, I have been trying to adjust the quadmesh settings but its not localised enough.

So I want to prepare a standard simplification/smoothing of the inputted mesh edges which reduces how quickly and steep the edges curve up? Are you able to kindly recommend how I could do this? I don’t want to change the inner surface of the mesh I just want to subtly simplify the edges based on maybe a max radius?!

240421 - Intersecting curves.3dm (404.8 KB)

Any thoughts very appreciated!

you can try smoothing the mesh like this

Thank you Adel!