Okay, so I ended up solving my own problem. I would delete this but maybe in some distant future it may help someone else:
I went searching through my box of cables and stuff that I keep (since I never throw those things out, although I probably have little use for a bunch of DVI and Composite cables anymore) and pulled out the following:
An RCA to S/PDIF adapter, a 3.5mm RCA to 3.5mm splitter and a Toslink cable. I set this up to be 3.5mm RCA splitter to RCA in and Toslink out to Digital-In in the Soundblaster Z. Now there is perfectly crisp digital audio coming from the mini and no feedback.