We've been lucky. Only minimal changes are needed to get the program to comple and run. The compilation error was caused by a missing #define which is easily fixed. Then it is a simple matter of changing the hsync and vsync pins as the mega has them mapped to different pins.
Simply change the code near the beginning to this:
#define UCPHA0 1
const byte pixelPin = 1; // <------- Pixel data
const byte hSyncPin = 9; // <------- HSYNC
const byte MSPIM_SCK = 4; // <-- we aren't using it directly
const byte vSyncPin = 12; // <------- VSYNC
hsync is now on pin 9, vsync is on pin 12. I have not been able to test I2C yet. (Incidentally, MSPIM_SCK isn't connected to an external pin on the Mega - this does not affect the functioning of the code.)