Aha! I finally puzzled out why page-turns on the KT seemed to be unreliable!
Much of my reading recently has been outside, catching some rays on the deck.
In direct sun, the (Black) NT warms up considerably, and it seems to diminish its ability to notice a touch or swipe - I had to repeatedly tap or swipe, when the first try didn't work.
When I began reading inside more, the tap/swipe turned the page much more reliably, so I construe that the infrared sensors probably get overwhelmed when the KT heats up from the sun.
I hadn't noticed this effect with the NT, because I tend to use its buttons instead of swiping, while reading one-handed or sitting without a table to rest the e-reader on.
So if you are working on your tan, try to keep the KT cool and out of direct full sun - it will work better...