Hmmm, not as easy as it sounds, but it should be possible at least with flattened files. It seems to me you could create an action to:
1. Convert the file to a Smart Object. This is necessary to "wrap" and protect the original, so that clipped (out of gamut) colors can be regained, and also to minimize the degradation from multiple conversions.
2. Convert from original document space to the old monitor profile. You'll want to change the RGB numbers in the original file, and the change should be equal to the difference between new and old monitor profile. But you can't do that directly in the original color space because the numbers will have a different meaning there.
3. Assign the new monitor profile. This will change the appearance to what it should be.
4. Convert back to the original document space.
5. Rasterize the Smart Object.
No guarantees and I may have missed something or messed up the sequence. I'd recommend saving duplicates until you're confident that it works. Then you can run the action in a batch or use the Image Processor.
EDITED because I see no way to do this with layered files (adjustment layers are color space specific).
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I managed to somehow test this by using an obviously wrong profile for one monitor. It seems to work. And even if you end up with a set of flattened files you at least have a reference to correct the originals to.
And of course the obvious point: no matter how alternative your process is you'll always be better off with full color management. Simply out of curiosity I keep looking for scenarios that could justify a non-color managed workflow, but it's shot down in every case. It just works.
Just so we're clear on how Photoshop uses the monitor profile, it's pretty simple: the document profile is converted to the monitor profile on the fly and sent to the display. If the monitor profile is not an accurate description of the actual monitor, it will look wrong.
The calibration software however will do two things: first it will calibrate the monitor to a set of basic parameters (white point, gamma, neutral color balance). Then it will make the profile (the description) of the monitor in its calibrated state. So you won't get a perfect match between Photoshop and apps that are not fully color managed.
Thnak you for your help. All of these images are 100% finished, and I know I will not be continuing with them in the future. So long as they look as they were, I'm fine with them being flat.
FYI gum printing isn't as exact as some other processes, and is very flexible. Having full color management just isn't as essential as something like cyanotype or platinum, often a gum printer will use manual abrasion to lighten areas, or might apply second exposure to darken areas. It would be cool to have a CMYK profile for soft proofing process seps, and eventually I'd like to get there.