Thank you friends for rallying round.
@Odinbc "Right tool for the job." I fired up imagej (strangely, I didn't have it on this my main machine, but use it somewhat regularly on the others). Analyze->Histogram brings up the window with a promising-looking "Live" button.
I can draw a selection of my desired size and aspect, and drag it around with the "Live" button activated, ImageJ shows me a real-time histogram and identifies the min and max at the same time. (Just like in my dream.) Thank you.
Edit: BTW, I discovered that holding the Shift key will maintain the aspect ratio as the selection is resized with the mouse: important feature for me.
@Ofnuts Bringing it to GIMP. [For the sake of archive-ness] I installed the script (after making it executable and looking into it to see its registered location) in plug-ins/, ran Filters->Script-fu->RefreshScripts, but didn't see it (because I think I didn't scroll down far enough), but found it right away after restarting GIMP: Filters->Find min and max in drawable...
I create a selection initially, or move it, and then select the minmax filter, and the min/max values display for me on the bottom-most (sorry, don't know the name) line of the image window, but with a "Danger" sign (red/white triangle with '!').
Incidentally, the high value reported is off by -1 (e.g., 254 instead of 255), and the low value is off by +1 (1 instead of 0).
This is a huge improvement over the nothing that I had before, and is plenty useful as it is, but does require repeating the filter after each move instead of updating the min/max continuously during movement. [Again, just recording this for archival purposes. As you said, "quick hack", which for me demonstrates the feasibility, for which thank you.]
@SaulGoode
Whene'er I have ventured into ScriptLand, I have so far, always, headed perpendicularly away from the Great Gray Mist. ;^)
Thank you. Again, if you'll leave them here, one of my future selves is sure to come hunting them (after we get over our irrational fears).