The sketch uses touchcontroller instead of touchscreen. I did not find any place to adjust the touch sensitivity, but I may have missed something.
I breadboarded another setup and it worked fine, so I suspect the LCD is bad. Not looking forward to unsoldering the old LCD!
I did order another kit, which I will use for the final project and use the other two LCDs for experimentation. The faulty LCD works fine as a display only, just no touch screen.