I tried the version you recommended, Shadow, and it worked! Thanks a lot!
The cards are exactly the same, but I took one out so I would just do one at a time (I didn't want to deal with software issues).
With the newer version of nvflash, I typed in "nvflash -4 -5 -6 9600OC.rom" as it said in the recent TH article, using the same card (different manufacturer, though). Then I got the "Supported EEPROM not found" message.
Then I tried Shadow's method in his wonderful guide and typed in "nvflash --protectoff" and I had to choose what I wanted to unprotect: something I could not identify (I can't remember exactly what it said) or the clearly labeled 9600. I chose the latter. Then I typed in "nvflash 9600OC.rom" and I got the same message. I tried both methods several more times with the same result.
I then tried the older version and typed in "nvflash -4 -5 -6 9600OC.rom" and it worked.
I think (I don't know and am merely speculating) that the new version was seeing two EEPROM's that could be flashed and did not know which one I wanted, so it went with the first one (possibly the motherboard) but could not flash because it is not compatible with that one (it is not "Supported"). Perhaps the newer version recognizes not only more cards, but also motherboards.
The card works fine so far except for the fan speed (which I could change in RivaTuner).
I'll get to the other card tomorrow after I find its maxes.
I really appreciate all the help so far. Thanks a lot!