I don't really think that the screen get garbled due to timings or ESD.
I never supposed that anybody could connect something directly to an MCU pin with a half-meter wire, but they did it... And that single thin GND wire (yep, only one of 20 wires is a GND) only aggravates the situation.

This garbling issue can be fixed by adding a serial resistor to each MCU output connected to the LCD. These resistors should be placed as close as possible to the signal source (i.e. to the MCU in our case case) and by routing a reliable ground wire to the LCD board.

But I'm to lazy to do all these things, so I've just cut the LCD cable (there are two cables - one for LCD and power, and another one for SD card) at the mainboard side and solder 47 Ohm resistors there. This appears to be enough to get rid of LCD screen garbling.
lcd1.jpg