Thanks for your idea. Based on other Denafrips DAC owners' experiences, it seems to be an Apple OSX and/or USB issue. Sometimes it is correctable by making changes in OSX versions; sometimes not. There is a known issue with 2014 USB settings(?) in Mac Minis.
I'm going to try connecting it to a brand new MacBookPro next week to see if it is compatible. Really, this whole experience is frustrating. I'm tempted to run out and buy a cheap Windows PC because I know it will work without a hitch. A new MacBookPro will set me back a helluva lot of cash.
[I had intended to buy a MacBookPro for other reasons before this happened.]
I decided it must be something to do with settings somewhere in my OSX, so I peeked into my 'Audio Midi Setup' 'Audio Devices' toolbox. Nothing appeared to be wrong, but I clicked on Combo384 Amanero anyway just to poke around. The format was set to its highest setting of 768000Hz. CD quality is 44100Hz, so I selected this just to try. Well, what do you know? My issue is fixed.
Now, I assume my output is limited to a max of 44.1kHz with this setting, but there are other settings which I can experiment with.
I've adjusted the format to 192000Hz with no discernible ill effects.