I love my Squeezebox, so I'd recommend that.
If you want to go wired though, sending a digital signal and then using a DAC should work good too. I don't remember the details on cable lengths, but somehow I thought that coax cable was better for long runs than optical (I well could have that backwards though).
Assuming coax works, you should look at Canare's micro-coax cable: L-1.5C2VS. It is smaller in diameter than the Belden 1804a silver cable stock people use for mic cables (that is, really small, on the order of mic active cable diameter). You should be able to make a coax cable using this stock and then pull up the carpet bit by bit and run the cable under the carpet between the carpet tack strip and the wall.