Thank you Brian! Construct > Curve > Project is just the ticket for the parallel case.

Re:
> Can the script "ViewRaysThroughPoints2" be modified to project many
> arrayed points on the Curve, Through the projection point, onto a
> Plane? With the result a line on the Plane?

I need this to be pretty accurate, so if I were going that route it would probably have to be iterative rather than a uniform array. I worry that doing that well might be complicated. And it also seems like reinventing the wheel since the Tan points from the snapping mechanism when drawing a line from the point to the curve are basically what I'm trying to get. I just haven't figured out a way to get them using a script without manually moving the mouse around and actually snapping to them.

- Peer