My apologies. The screen is 8-bit parallel. The screen does not use SPI. But the SDcard does use SPI.
Yes, a 16-bit parallel Mega2560 display Shield will use PORTA, PORTC digital #22-37. This will work at a reasonable speed if you use a sensible library like Bodmer's TFT_HX8357.h library.
But your existing shield will work pretty well with an Arduino Due clone.
Most importantly, you can display JPEG images from PROGMEM.
David.