I haven't seen it recommended here, but a few months back, I picked up an M-Audio DiO 2448 on eBay for about $25. It's not the highest end, since it only supports 24 bit/48kHz. However, it does have both optical and coaxial output. When you're ready for the next step, it'll send a clean signal to an external DAC.
It works fine with ALSA (Linux) and I believe it has full support in Windows.
If you can get a cheap DiO 2448, it'd be a small budget stretch to pick up a Gilmore Lite which goes for $299. If you're handy with a soldering iron, you can build a Dynalo (same thing, more or less) for around $100.
Your HD-650 would sound great with this setup.