Audulus Bluetooth Quality Fix!!!
I finally figured it out after obsessing over the issue for the last few days! This might be useful for other users too, which is why I am posting the solution to my issue. I should also mention, I have only figured out how to fix this on Mac, as I am not aware of any way to force a codec change or put a headset in output only mode on iOS (Perhaps this could be a feature that Taylor can include in a future build of Audulus?).
So the quick answer is to follow the instructions here: Bluetooth Force Codec.
For anyone with output only headphones, that should solve your issue. If you have a microphone too, and you’re still having audio quality issues, read on.
There was also one more step for me to take. The reason the sound was so terrible and clipping after enabling the above is because the headphones all have one thing in common: a microphone, which some people might wish to use as an input. The microphone makes the headset stick in a low quality codec profile (from what I understand) because it needs to use the same channel for input and output at the same time, or so it decides without informing you.
Navigate to System Preferences > Sound > Input and double click on the option for Internal Microphone and you will hear an instantaneous change. Your bluetooth headphones should now be in either AptX or AAC codec mode, and the quality issues will be resolved, barring some serious wireless issues you may have outside the scope of this instruction set. I hope this will help others, as well! 
@biminiroad - even if I had figured out the codec thing, I would still be having issues, if not for your advice about polyphony. Thanks so much for replying and helping me to get this resolved! 