Playing with stuff, so not too bored yet.
For the time being just switch the get closest point node for a get closest location, remove the array pick (no need since get closest location returns a single location) and you should get the mesh following closely.
It's still not in full what the cage deformer does, that's a bit trickier with the context limitations, but it might get you where you want to be in terms of speed and overhead (lack thereof).
Scene attached if you're that lazy you need one :D, but it really is a matter of swapping a node and deleting another.
359f1058a29caf8e6d146723c18fd652.zip