Convert multichannel image to CMYK while preserving appearance of multichannel colours

Amazing – thank you very much. This method works. As you say, the colours come out "wrong", but they're a close enough approximation to work with.

How does this method work? Does the process of creating four new channels somehow fool Photoshop into thinking that it's a CMYK file to start with?

Many thanks for this. What you've written in your first paragraph is what I'd feared. I'm surprised, though, that there's no facility in Photoshop for seeing the multichannels as if they were separate pictures which could then be blended together within a CMYK or RGB mode. There are examples of pre-desktop publishing graphic design wherein someone might have plates made according to C, M, Y and K, and then substitute other inks for use with each of these plates when they were actually on the press. That's all I'm trying to do, and it seems odd to me that Photoshop can't cope with something that could be done easily enough before computers were even used for design.

Re. the screenshot option: I'd wondered about this, but surely this would only enable a low-resolution result?

Is there any workaround whereby the separate multichannels can be exported as though each was a single-colour layer instead of a channel, then recombined in Photoshop to get the looks-like-multichannel result?