Flow along surface Shape Change

I am using Rhino for stone carving and CNC toolpath, but when I am applying the flow along surface to the shape to bend the subject on the curve, it is getting stretched or an unwanted shape, so how can I resolve that?

Also, the file is quite large so I am sharing the screenshot for this only

In this the top view shows the shape as original, which I am bending, but in the perspective as well, the top view shows the same issue, where the shape is changed

The shape will be changed in direct proportion to the isocurve relationship between From/To surfaces. Your target surface appears to have been built so the isocurves are not perpendicular to the edges.

SO I have to add the slash while applying the sweep shapes, so this proportion will change, or what is the solution for this?

my recommendation is to handle the green circular inner part separate from the blue elements.

you will always have a deformation - the circle will become some fancy distorted oval shape.

check the help for _flowAlongSrf (<- linked !!)

… and also check this forum for other topics about this command.
make sure your target surfaces has nice parametrisation - you might need to rebuild it.
FlowAlongSrf happens in parameter-space

what this means can be easily show by flowing “Tom”-Curves from one rectangular surfaces to another rectanglular surface with uneven distributed Controlpoints:

hope this helps - kind regards - tom