Hi Tom,
I checked your code and you did really impressive work.
I just would like to know why you don't inherit from the SPI class to obtain the SPI management done by the SAM3X SPI Peripheral.
Is it because the shield could be used without using the SPI dedicated pins?
In case of you would like to use SPI, it could be useful to add a small buffer in RAM and then use it as DMA input for a given maximum drawing object size.
That way, you should greatly improve the framerate, I hope.
This could also bring an accelerated bitmap blit from Flash/RAM to LCD, couldn't it?