Tom, excellent work on making both the library and adding Due compatibility. I myself have pulled my hair out since Sunday looking at the code for 9 bit SPI addressing for Adafruit 1.8" and 2.2" SPI displays (which use different low level but similar code bases). Found UTFT not helpful for SPI displays then found your code. You are the only person I have found to map the low-level SPI addressing on the Due to be compatible with anywhere near similar calls on the '328 Arduinos.
I'll be looking to see if I can update the Adafruit code for their HX8340B unless you object. Arduino Code | 2.2" TFT Display | Adafruit Learning System, GitHub - adafruit/Adafruit-HX8340B: Adafruit 2.2" TFT with SPI interface and microSD card holder
Update: I've suspended the work for now. It would be helpful to see a diagram of how you wired your displays along with the test program to check the pins used. Mike