It really appears to be a problem of signal levels. I am using a different USB audio adapter and it is not as bad as in your case, but the output from the computer is much more quiet than let's say a CD or radio on the same head unit volume setting (and Mac at maximum). Fortunately my head unit (old Sony CD XA 900) does have a signal level correction for the Aux input. I have to set it to +4dB to get the computer ouptut to the same loudness as the built-in tuner or CD.
Just to be sure - are you connecting the output of the USB adapter directly to the amplifiers or do you run it to head unit's AUX input?