On more thorough research, it mostly seems to be a hardware problem. At least, part of it.
When the touchscreen freezes up, it seems the sides of the phone itself are somehow pressing on the edges of the touchscreen, thus disorienting it. Apparently the solution is to press the edges of the phone itself so that the internal pressures are realigned, and up to now this solution seems to be working!!
So at least partly, Windows is acquitted.
(Doesn’t explain the extremely slow response, and the occasional freeze-up, though.)