promacjoe:
According to the schematic, the Arduino due uses a NPC1117ST33T3G 3.3V regulator. According to the datasheet, this regulator is rated at 1A. since it is a linear regulator it generates a lot of heat, so replacing this regulator would not do much good.My thought was to replace the power supply header on the adapter board with one that is extra long and bent to provide a place for external connectors. By snipping off the 3.3V pen that would plug into the Arduino due board, you would isolate the power going to the display. Now it can be connected to an external PWM power supply adjusted to 3.3 V. This type regulator does not get as hot and can produce a very stable voltage. And since you replaced the entire power header, you get access to the VIN,GND, master reset, 3.3V "IOREF PIN low current" and 5V power from the Arduino due as well.
This should eliminate the heat problem caused by pulling too much current from the due board.
promacjoe
I hadn't thought about it to that extent yet but it's the back light that is drawing most of the current so with that in mind I was going to simply use the existing back light power connection to driver a transistor to switch a separate power supply to the back light from a second USB socket.