Noise on stereo summing circuit from LED's
This is not really an answer, just help in identifying the problem.


  the signal noise also vanishes if I disconnect the outputs of the USB sound card.


This means it could be a ground loop issue. So, please try this:



This means you desolder the end of each 470R resistor from the wire that goes to the signal wire of your TRS jacks, and solder them to the ground wire of the same jack instead.

Since signal is connected with ground, no sound should come out of the amplifier, and you certainly won't hear any PC audio.

If you still hear your LED PWM in the loudspeakers with this arrangement, it means the potential of "ground" is different between all the points labeled "ground". So "ground" which should be 0V contains audible signal voltage instead. The cause can be high current (like your PWM LED current) flowing through ground wires, which do not have zero resistance, and this creates noise voltage.

If this is the case, then the problem must be fixed at the source, and the chopped LED current should be routed away from the sensitive parts. How to do that depends on how your LEDs are wired, how the controller is wired etc, so you will have to post more info and schematics. 

But at least this simple test can narrow it down to "ground loop" or "something else".