Your best bet for Arduino Due would be adapting my contribution to Neopixel. It's simple code. You probably only need to tweak the timing parameters, ideally using an oscilloscope or logic analyzer, but maybe trial-and-error might work?
In Neopixel, the 96 MHz parameters for Teensy 3.0 are probably very close to what Due needs at 84 MHz. They might even "just work" on Due, since the speeds are so close. Due has better faster flash memory caching than Teensy, which might compensate or even over-compensate for the 12 MHz difference in core clock speed.
I took a look at your code, and I'd like to try to port it over to use on the Arduino Due, but I'm confused by some of the following statements:
That OctoWS2811 code is very specific to the DMA controller on the Teensy 3.0. Arduino Due has very different hardware, so the code is not compatible and not easily adapted.
For documentation, here is the datasheet:http://www.pjrc.com/teensy/K20P64M50SF0RM.pdf
The TCD registers are documented in chapter 21 beginning on pin 333. They're extremely complex and not a good beginner level project! That's why I wrote OctoWS2811... to put all that difficult stuff into a well documented library that makes these types of projects easy. OctoWS2811 is designed around the Teensy 3.0 hardware and probably would be more difficult to port to Due than simply writing a brand new library from scratch.
However, Neopixel should be fairly easy to port to Due.