Sorry if I am being dense, but I'm still confused on the threading.

The fixed/drive-side cup says "Right Lock" with an arrow pointing counter-clockwise. To remove it, I had to turn it clockwise. Which means that pedaling would loosen the threads.

So the drive-side cup is right-hand threaded or Italian threaded, right?

The adjustable/non-drive-side cup says "Left Lock" with an arrow pointing clockwise. To remove it, I had to turn it counter-clockwise. Which also means that pedaling would loosen the threads.

So the non-drive side cup is left-hand threaded, right?

That doesn't match any entries in the table on Sheldon Brown's site: http://www.sheldonbrown.com/gloss_ta-o.html#threading

The only entry it partially matches is English, but with the threading reversed on each side.