Target geometry output of Pull Points component

I have a large amount of points and curves (geolocations and streets) and want to find the closest point to each point on the street network, as well as the curve of the street network on which this point lies.

I thought the Pull Points component would be useful for this, as it very efficiently finds the points in question when fed the street network as input geometry. However, it does not pass out the information of which object of the geometry input that the points has been pulled to.

I can't think of a good way of getting this without basically rewriting the Pull Points component, and then adding the additional "target geometry" output. Using "ClosestPoint.distance == 0" is not an option as I would have to check this for 1e6**2 point/curve relations.

Am I missing something here?