It turns out a bug was preventing UVD from being properly used with the RadeonSI driver. Christian König at AMD finally was able to figure out the bug today and explained, "Sorry that it took me so long to find this. It's a rather simple issue that the IRQ support for UVD on SI wasn't activated. With this patch in place I now get 52fps with 1080p H264 decoding."
This new patch that came up today will show up for the Linux 3.14 kernel and should also be back-ported to the stable kernel releases given it's a bug-fix. It's also recommended to be running the very latest Mesa driver code whenever dealing with the open-source RadeonSI driver for AMD's GCN graphics hardware.
More details on the RadeonSI UVD issue that was solved today is documented via Bug 71448.