UPDATE: First off, thanks for all the thoughtful responses and suggestions...
Second, I took a water sample in to Caeser's today to have them test everything, just to see if maybe I had a bad test kit that was hiding something. The good news is that almost everything tested ok; the bad news is that one item did not... and it almost certainly explains the problem, both in terms of current conditions, as well as the timing as to when the problem started!!
In a nutshell, after visiting Caeser's (and then researching the possibility a bit more online when I got home), it appears that my swing arm hydrometer has most likely been giving lower and lower readings as time has gone by (supposedly due to salt crystallization on the arm - it IS pretty old, and I saw this phenomenon mentioned a few places as a possibility).
In the old days, I kept my salinity on the lower end of what I thought was acceptable (around 24), but when I first posted about the original round of die-off and shared my numbers, was told by a number of folks on here that it was "a little too low, was probably causing the die-off, and should be closer to 26 or 26.5"... so I went ahead and slowly raised it.
HOWEVER...
I'm guessing that the die-off at the time was actually due to my salinity already being TOO HIGH... and thus, raising it made things even worse!!
As it stands, my current hydrometer is showing 26... but my new hydrometer (which admittedly has not gone through the recommended 24 hour "seasoning" period yet), is showing 32 (and Caeser's said 30.5 based on their visual hydrometer)!!!
What a crappy reason to have lost several hundreds of dollars worth of coral over the past 2 years, eh?!
Anyhow, no guarantees that this is the problem... but I'm hoping that once I've brought the salinity back down to where it is supposed to be, things will turn around (and "blue bucket salt," NO3, and "hard to detect forms of phosphate" will be exonerated

).
Thanks again for all the help you guys provided - I'll be both angry and glad if it turns out to simply be a case of literally cooking things chemically with salt due to incorrect hydrometer readings!!