Since I solved my problem, I haven’t pursued this issue further, but here’s my guess of what was happening. (I’m going by memory from some time ago, and haven’t done any subsequent tests, so don’t put too much reliance on my guess.)
My Acer is my primary display. My NEC is my secondary display. If in Vista Color Management I set my Acer profile for my Acer, and my NEC profile for my NEC, when I open PS on my Acer and drag my photo to my NEC, PS uses the Acer profile for both my tools pallet on my Acer and for the photo I dragged to my NEC. Not good. On the other hand, if I set my NEC profile for my Acer, when I drag my photo to my NEC it looks fine since PS is now using the NEC profile for both the PS tools pallet on my Acer and for the photo on my NEC. Problem solved.
I discovered that whenever I create a new profile for my NEC, SpectraView deletes the old NEC profile and, in Vista Color Management, sets the new NEC profile as the default profile for my primary monitor (my Acer), but not for my secondary monitor (my NEC), so my NEC no longer has any profile assigned to it. No problem with PS. (See the prior paragraph.) When I open LR on my NEC, however, -- big problem. LR doesn’t have a profile assigned to my NEC to use.
My speculation is that for LR I could use my Acer profile for my Acer, and my NEC profile for my NEC, in Vista Color Management, especially if I always open LR on my NEC. This setting doesn’t work for PS, however, as described above. So, to get both LR and PS to work properly, in Vista Color Management I set my NEC profile as the default profile for both monitors, and every time I update my NEC profile I manually set that new profile as the default profile for my secondary monitor (my NEC).
I’m not sure if you can follow this rather convoluted explanation, nor how relevant it would be for anyone not using my same configuration. In any event, for what it’s worth, this is my speculation for the cause of my problem.