The vertices of the plane should be the selector for the edges, then the nearest edges of the mesh islands should be selected an subdivided by one and in the next step, these subdivided point should be slide on the edge to the nearest position of the selection points.
This node setup is used to ensure that the points do not go beyond the edge length (vector projection).
This node setup is used to determine the position on the edge (vector point projection).
That is the hole node tree.
The missing top nodes are the vector projection.
The vector projection worked not really well and i don’t know how transfer the nearest point position in to an selection.
I am happy about some hints.