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Alright, well, I finally fixed this problem -- wouldn't you know it. The problem was indeed that PS was using the wrong monitor profile. Just in case anyone else has a similar problem here's what I did.
1. In Edit > Color Settings, look in the pulldown for working space, and scroll to the top of the list. Look for Monitor RGB. The profile name to the right of this label shows the profile that Photoshop is using. When I did this, I saw "sRGB IEC..." Okay, that seemed wrong, because I had created and saved a profile for my fancy NEC monitor. So, ...
2. I Went to Windows > Start > Control Panel > Color Management > Devices Tab. I have two displays on my machine, an ordinary one and my NEC display for photo editing. There's a pulldown to select the display to be configured. For the ordinary display, I did not have "use my settings checked." For my NEC display, I had "use my settings" checked, and I had my custom profile selected. Then I went to the Advanced Tab....
3. Ah Ha, the system default profile is sRGB (I guess as one would expect, given that sRGB was precisely defined as a generic monitor color space). So it appeared that what was happening was that Photoshop was picking up the default sRGB profile, not the profile that I *thought* I had designated for the NEC display. So, ...
4. I went back to the Devices tab and selected my NEC display. I had already checked off "use my settings" and the "profiles assocaited with this device" already listed the custom profile that I wanted (the system and Photoshop) to use. Mystery ... why wasn't PS picking up the profile
5. Ah Ha (again). There's a "Set as Default Profile" button at the bottom of the Devices panel. I clicked that and suddenly the word "(default)" appeared next to my profile name. I went back to the Advanced tab expecting to find my NEC profile listed as the system default. Nope: sRGB is still listed as the system default. But I figured I might as well open PS again and see if explicitly setting my custom profile as the default (for the NEC display) made any diffference...
6. Voila the colors are now what they should be. Halleluja. So I go back to Edit > Color Settings > Working Space, and I go to the top of the list and look for Monitor RGB, figuring I'll now find the name of my fancy custom NEC profile. But noooo. It still says sRGB!!!
In any case, PS is now obviously picking up the right profile for this monitor, but still displaying the name of the system default profile.
What's the lesson? Neither Windows or Photoshop is well designed in this area. Windows seemed as if it had associated the right profile with the NEC monitor, but at least as far as PS was concerned, it hadn't: not until I *also* clicked the "set as default" button for the profile on that monitor. Even when I did this, although PS clearly then picked up the right profile, it still showed the system default profile for Monitor RGB. Moreover PS doesn't reveal what monitor profile it's using under a "Monitor Profile" tab ... no, you have to pull down the "Working Space" tab and then scroll up a few screens to find out this information. Forty years after the PC was created you still need either a PhD or Autism Spectrum Disorder to figure out these freaking software systems **because their designs still suck** (Windows way more than PS, but neither is perfect).