Yeah, I think a selective bloom pass would be the easiest way to get the shiny dots.
However, you might run into a problem with anti-aliasing due to all the small thin lines. When you use a post-processing effect (at least with WebGL1) you have to disable the built-in AA and use a post AA pass such as FXAA or SMAA.
In my experience these don’t always give nice results with thin lines. The examples I was testing with were architectural models so the lines were largely vertical and horizontal, you might have better luck here since your lines are at many angles and animated.
By the way @prisoner849, your selective bloom examples don’t use AA at all, right? They look surprisingly clean considering.