I do not support any controllers with ID = 4288 (0x10C0)
You do not need any software changes for Nano. Simply wire all the Shield pins to the corresponding 3.3V, 5V, D2-D13 and A0-A4.
In fact I have two Nano Adapter boards. i.e. Arduino headers with a socket for Nano.
I can run regular Shields with Nano-328P, LGT8F328P, NANO-EVERY, NANO-THINARY
I strongly recommend that you buy a proper Uno clone i.e. with Arduino header sockets.
Or buy a Nano Adapter Board. i.e. with Arduino header sockets.
The current Mcufriend Shield design is WRONG. It powers the backlight from the Arduino 3.3V pin which is WRONG. The original Shields had a 3.3V regulator on the display pcb which was powered by the 5V pin.
The Nano 3.3V pin comes from the USB chip. It can not supply much current.
David.