Good link! I've both forwarded it on, and will study it when I have some time later.
The Cauchy matrices remove the need for a table lookup to do the Galois multiply, replacing it with pure XOR. Together with other optimizations, this gives nearly 3x-5x more coding throughput for the same (17,3) parameters, assuming you're still using your open-sourced JavaReedSolomon in production. I don't know if Reed Solomon coding throughput is a factor in your rebuild times?
It contains optimized Galois Field multiplication, resulting in Reed Solomon (both Vandermonde as well as Cauchy) at multiple GB/s on a modern x86 CPU.
Still, I doubt that the Reed Solomon coding speed is the limiting factor in their rebuild time. There is a mention of a 6-day duration, so even with a very slow Reed Solomon implementation ( ~ 100 MB/s) that should not be a bottleneck for a 10 TB drive rebuild (assuming a distributed rebuild approach, not a traditional RAID style rebuild).