I'm also curious to know if the TV has any sort of digital output. If it does then finding some way to make use of that might prove to be the most advantageous solution.
I ain't at home so I couldn't check. Though I just downloaded the manual for my TV and it does indeed have an optical digital out. However my receiver only has 1 optical input port and it's already in use...
I would say it's much easier to work around that problem than to get digital out from the RPI... I assume the occupied digital in can't be switched for coaxial for some reason?
If so, $15 will buy you a solution.
You should, however, test this before hand to see if surround sound will be passthrough the TV from HDMI to the digital out. It's a common problem, and it's a reason many people don't use the digital out from their TV.