I used a public domain image to demonstrate this effect. It's available in the NYPL public domain collection. I've gotten this effect about as close to my desired goal as I know how. The only step I couldn't get to work was saturation masking, so that the line art doesn't also go through the half tone process (particularly noticeable with thin line art). I tried using Set Matte with the source art's saturation, but white and black get assigned different levels, despite both having a saturation of 0 in the color picker.
It's 3 layered Half Tone effects (one for each color channel) at different angles, matched to what I could find online for screen printing info, with separation of line art, and masking of areas of pure (or mostly pure) white. This was one of the first things I figured out how to do in HitFilm. If you layer a Diffuse grade over this, it gives it the feeling of smudging over the years (especially combined with a plane in Multiply mode the color of aged newsprint) or being printed on wax paper, like those old Bazooka Joe comics.
Any advice on the saturation masking would be welcome. Thanks for checking this out!