Arduino DUE How to Direrct Port Access?

"As I understand it you can't simultaneously set some pins high and some low, you have
to set some high and then others low, or vice versa, using two instructions."

Yes, you can. The magic trick is to write directly on the register status rather than on
the SET and CLEAR registers. Here is how:

PIOC->PIO_PER = 0x01FF; // Configure PORTC to PIO controller, pins 33-40
PIOC->PIO_OER = 0x01FF; // Enable PORTC to output
....
PIOC->PIO_ODSR = something; // Write something on pins 33-40.

The Output Data Status Register (ODSR) is available for reading and writing (under
weird circunstances). However, this does not happen for all the registers; that's why
there are so many SET and CLEAR status registers. Of course you can add also bit
masks in order to avoid writing on protected pins.