You can use USB through your Touch with EDO if the DAC/converter supports the USB Audio standard. I use a Touch connected to a Wavelength Wavelink HS USB converter in my bedroom and it sounds great.
However, I think the Mac Mini is the best solution, which is what I use in my main system. The Logitech playback software sounds fine, but you can get better sound with other software. I like the Mac Mini because it is extremely quiet and supports both OS X and Windows natively with Bootcamp so you get the best of both worlds in terms of software. I think JPlay (Windows) and Amarra (Mac) are the best sounding, but both interfaces rather suck, so I reserve those for critical listening and mainly use Squeezeplay (this would be useful to you so you can keep your LMS library) or Foobar2000 with an iOS or Android remote app. Having a smartphone/tablet is soooo convenient and is well worth the modest cost for this function alone.
To me the USB converter is a key component and is a worthwhile investment.