"So it seems the DAC and the amp are functioning properly independently, but something screwy happens when they are used in conjunction. And the DAC is producing some signal doing its algorithmic thing that the Jolida is picking up on."
"To Bill_K: When the DAC is used with a different amp (a pair of Audioengine 2 powered desktop speakers), the ringing stops. But when the Jolida is used from the headphone jack of the computer or from an ipod, there is no ringing either. So each component individually seems to work just fine, both the DAC and the Jolida seem healthy. But something about them working together makes bad mojo."
I'm still not sure what the problem is, but reading those quotes made me think of a couple of other things you can try. First is a different music player. I assume you are using iTunes. Try Quodlibet for Mac. Its open source, so there's no charge for it. I can't say for sure, but you'll probably like it better anyway. It plays more formats and is a much better tagger than iTunes. Second is, how are you connecting your Mac to your dac? To get digital output, you an only do it 2 ways; usb or Toslink using a special adapter that plugs into your headphone jack. I'm assuming usb because its the most popular option, but a lot of people do use the Toslink option. And third, how do you connect your dac to your to the Jolida? This is really important because you have a balanced dac while the integrated is single ended. Even if you are going SE out on the M51 to SE in on the Jolida, you may have to do something to your M51 to make it work properly in SE mode. If you are using balanced cables and adaptors you still need to be very careful. Not all IC that have XLR connectors are balanced. Internally, the cables may be SE. There's a lot of confusion on this because when most people see IC's with XLR connectors, they automatically assume they're balanced. That's not always the case.
It also wouldn't be a bad idea to call NAD. Its very possible that you're not the first person to have this problem.