I didn't mean the voltage was a problem, I meant that if you put a linear regulator between the SMPS and the audio player you should be able to filter out a lot of that power line noise. If that means SMPS at 12V and regulator lower (there needs to be some drop out voltage), then that works fine. If it means an input at like 13.5-14V from the SMPS and a regulator down to 12V that works fine too. Maybe if your SMPS has an output adjustment potentiometer you could turn it up to use a regulator in between.
Earthing can often be problematic in audio stuff, but unless your SMPS is ground referenced, there wouldn't be a difference between the bench PSU and the SMPS for that. It does sort of sound like really loud ground hum, though - make sure all of your circuit grounds are actually attached to each other, and if possible, attach them to each other at the same point.