Harshness isn’t in cables. Good cables can reveal harshness but don’t go back to bad calbles to mask it. Fix the source. You didn’t mention your DAC.
Also your tolerance for harshness can change. I fought harshness for a while with an amp. Sometimes it would disappear and life would be great. But it would come back.
Internet radio may be low res and thus you get rid of harshness.
So I’ll say harshness is a sign of progress toward a resolving system.
One thing you can investigaate is can you turn down the output voltage on your dac. Some good dacs have this feature.
Jerry