Hi, all.
Mike - yes, aligning the tubes to the correct direction is a challenge of this method. I just make the best estimate I can. I'm anchoring one end of the line as pictured and the other end will be another tube (hopefully at the right angle, also) into which I CA glue the end of the monofilament, holding the line as tight as needed to completely straighten it. If it's a little loose, I can tighten it using a hot soldering iron held close to the line, but of course, this presents risks also. I'm also flattening the end of the monofilament slightly with pliers to provide a non-round shape that should increase the holding strength of the mono and keep it from being pulled out.
davec - I don't hesitate to modify cheap tools to accomplish a task. In this case, I cut a groove using a Dremel cutting wheel, into one side of a pair of tweezers to be able to hold a round object.

The end of the tube was flattened, which prevents the drill from wandering when drilling. I hold the tweezers as still as possible, resting on the wooden block under the drill and then lightly run the drill down into the tube.

Hope this explains how I'm doing this.