OK - So far it all seems inconclusive. I can't figure out why the one computer failed to run on the UPS the other day.
On both computers I ran Prime95. The UPS's reported that this took the original 34 watt loads to 86 watts. Both computers performed very consistently, fans ramped up as expected. I then ran the APC PowerChute Self-Test after the computer was running Prime95 and the consumption was 86 watts. Both UPS's passed. As I was a little frustrated that neither failed, I then did the "cord yank" test on my wife's UPS and the system still held up without a glitch.
It would seem at this point that the Skull Canyon-APC UPS failure I found is intermittent.
I'd like to get Intel's response on the Skull Canyon NUC's AC Adapter's compatibility or sensitivity to the APC UPS's stepped approximated sine wave output.