How can I correctly convert a CMYK Photoshop PDF to sRGB?

I'm working with an artist to create a comic, which will be printed eventually, but which is currently being serialized online. The artist is working in CMYK in Photoshop, on the theory that it's better to convert CMYK to RGB than vice versa, and we'll need both.

We'd like to generate a master PDF file for each page which can be rendered into a suitable image for the web and can be used for a print run. That is, rather than export multiple versions from Photoshop, we'd like to export a single file that can be converted to anything we'll need (using a tool like ImageMagick). But I can't seem to get the color to work.

(I can't reveal the whole page yet, so I'll use a piece that shows off the problem.)

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  Here's an sRGB JPEG he exported from Photoshop. This one looks the best to me, and I believe accurately represents the colors he wants.

  
  

  

  
  


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  Here's what I see (a screenshot) when I open his (CMYK) PDF in Preview.app on my Mac. (The artist exported it using Photoshop's "High Quality Print" export setting.) It looks all washed out and flat. This is not what he sees on his Windows machine; there the PDF looks like the JPEG.

  
  

  

  
  


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  Here's the same PDF, rendered in Chrome (another screenshot). My theory here was that Preview is funky, and a different renderer would help. It looks better, but it's not the same as the JPEG file.

  
  

  

  
  


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  Here's the PDF exported to sRGB through Affinity Designer (the closest thing I have to Photoshop). The colors are still wrong; they're basically the same as Chrome displays.

  
  

  

  
  


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  Lastly, here's one that I converted from the PDF to sRGB JPEG with ImageMagick. This is the workflow I'd like to use in the end, to automate everything. This one is wrong in a different way: it's all greenish.

  
  

  

  
  

Oddly, I accidentally created a CMYK JPEG in my first attempts to use ImageMagick, and it came out similarly greenish in Chrome, but bluish-flat in Preview, rather like the PDF looked in Chrome (but—wait for it—not as washed out as the PDF looked in Preview.)

My head is spinning. Clearly there's enough information in the CMYK pixels in Photoshop to render the colors we want, and clearly they can be represented in the sRGB gamut, because we have a JPEG that does exactly that. But to save our artist from exporting multiple files (and potentially getting them out of sync), all I want to know is:

How can I render an sRGB JPEG with the same colors as his, starting with his CMYK PDF?

Or, if that won't work, is there a variation on this workflow that would? Or, if this is all folly, what am I misunderstanding?