DAC card ... seems overly loud and distorted
IIRC, the distortion is common for a lot of the sound output, here is an example:
YouTube: New DAC Sound Card for Apple LisaThe pixel tracks on the screen is an indication of incompatibility... those bits are supposed to go into sound hardware locations.
However, I believe there were a few applications that had good sound with it; I think Dafax published a list of those.
Earlier in the video there are some MacinTalk examples that have pretty good quality.
As for too loud, that may be a hardware problem which may be adding further distortion.
You could compare your board with the one shown here:
LisaDAC Sound Card