I keep going back to that grounding thing, static or EMI...
Neither of the datasheets has any helpful hints as to what might be going on.
Maybe try hooking a 'grounding wire' up to the touchscreen to the LCD frame, first with a 1K resistor (maybe less), then maybe a direct connection.
I'm thinking it's some sort of static buildup causing the controllers on the GLCD to go nuts.
Maybe try it sitting on a regular character LCD and see what happens? Not that a touch panel on a character LCD is any good, but it might lead to something...