The Autochrome process has less "quality" than the Dufay process and I am quite aware that as Autochromes (or Dufay) images are enlarged, they tend to break down and become very grainy. Evan at 1:1, an Autochrome looks worse than a Dufay image.
There are ways to balance the sensitivity of a film to a screen using color filters. This would increase the chance of success somewhat.
For useful results the screen should be against the film, but in the above OP, I can see using 2 screens. One to replicate the original and one on the print material.