When I mentioned earlier that didn't work for me, I forgot to run update-grub. On my partition for Ubuntu 12.04, went back and did that, now audio comes over the Radeon HDMI port.
Mint 14 - no joy.
I'm taking the lazy (easy) way out. My new video card came in, the one with the Nvidia GT 520 chipset. With this card I learned that the nouveau opensource drivers will not output audio via HDMI, you must use the proprietary drivers. I downloaded and installed the latest drivers from Nvidia. I now have audio via HDMI on both Ubuntu 12.04 and Mint 14.
I found this article from Nvidia:ftp://download.nvidia.com/XFree86/gpu-hdmi-audio-document/gpu-hdmi-audio.html
Although they say it pertains only to Nvidia chipsets, I learned quit a bit about how and where to troubleshoot alsa sound; you may find it useful. They do talk about various bugs and in which kernel they were patched, and they give the links to these. The article is dated Feb. 2012, and some of the fixes they anticipate coming in the 3.2 kernel. Maybe they all didn't quit make it and that's the reason for the radeon.audio=1 grub switch in Ubuntu 12.04 / Mint 13.
I have an MSI motherboard that the RS880 is output from. In the BIOS I have selections for onboard video or pci. Because the onboard video always shows up as card0 in /proc/asound, I discovered that I needed to disable that setting in BIOS. The reason being (as I understand things anyway) sound needs to go over the same HDMI output as the video. The system will choose the first card it comes across, so as long as my onboard stuff was enabled, the output never made it to the nvidia pci card.
Another thing I learned; I read where a monitor needs to be connected to the HDMI port before the system will use it. I was not able to hot swap between HDMI ports. I had to power down, then up, in order to use the "other" HDMI port.
I imagine if you wanted to, you could get into the xorg.conf file and enable both HDMI ports (I'm thinking using more than one monitor). I don't have a need for this, so I'm not going to try.
So at this time, I'm not going to persue a fix for the RS880 issue. I didn't find the answer for that, but took a different approach to get my system working; thefore the title Closed not Solved.