this line comes out because it is still a single polygon,
it would have to be cut up slightly,
this divides the large polygon into smaller ones and avoids overlapping,
something like this see picture edges
edges.JPG
i don't know the other shapes
if they are very different this might not work
maybe it works if you add an inset after the shapeanimation
but then you have first desolve the edges inside the shape
see next picture clean_inset
if you do the shapeanimation only with the curve and then leave a curvetomesh operator active you can create the shapeanimation even more elegant with the curve and insert a small inset at the curvetomesh, that should stay stable.
see scene
curve2mesh_inset.scn
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