Morphing a mesh between two surfaces

recently i got some very useful help here, morphing a mesh from its border to another polyline. now i got a similar problem while morphing a mesh from its original surface to the flattened surface.
as i used to solve this task for a long time with applymesh in rhino, i posted a longer version of the problem here in the rhino for windows section.
i constantly encounter troubles with this workflow, so i am interested in a grasshopper solution that gives better results and attached the sample file here too.

the example is part of a running job, so any instant help is highly appreciated. thanks in advance!
applymesh_V2_V6_gh.3dm (825.0 KB)