@curaga - Thanks for prompting me to try that again. I'd swear had tried it once before, but maybe it was before I reset everything or maybe I just made some dumbhead error (maybe like neglecting to restart the daemon). In any case, it worked this time.
@GNUser - Thank you so much - your solution worked perfectly (once I executed it correctly)
@Paul_123, Rich and aus9 - Thanks to you guys I am now an expert in all things ssh- and grub-related... or something like that.
@ Rich - Would you please mark this topic as "Solved"
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FWIW, on that original USB stick that eventually wouldn't boot anything, I ran out of space on it and had to go free up some space before I could finish what I was doing and it was around then that it stopped booting. I know I didn't explicitly delete anything grub related, but I wonder if something got trashed or overwritten when the FS was completely full. If so, that would be either "alarming", from an fs point of view, or possibly just indicative of a cheap USB flash device - so its almost comforting to remember that the device was very cheap indeed.