Here’s a thought: you could copy the points into an empty spline object. First set it to linear and no intermediate points. So now you have your spline representing the deformed state. Copy the spline and project it from a top view onto the DEM. Copy the original (unprojected) spline again. Now (assuming you have Mocca) set up a Posemixer to morph the projected spline into the original spline. Finally, use the projected spline and posemixer splines in a spline deformer to affect the DEM.
It should work in theory, but if the mesh is really dense it could be painfully slow. Might be point order problems too. Anyway, worth a shot.