The 976 has output that would allow you to put a mini DSP dirac unit between it and your amps. Not the other way around. Use the 976 to decode the audio first, then let the mini DSP do it's job.
Looking at the miniDSP site, your only option under $600 with dirac only supports 2ch audio. As long as the Shield TV supports the device, it should stream 2ch no problem.
I'm not sure your effort will be worth it in the end though.