If the sound remains dark and murky, it suggests the sensitivity is set too low. I am leaning towards the idea that your pedal is faulty. I do agree with the idea of placing some sort of pedal before it, so you can hit it with a bit hotter signal. But it should work just fine with just bass, pedal, and amp/DAW. You could also try bumping up the tone controls on your active bass to send a hotter signal to the Mooer, rather than using a pedal.
Here is a Bass SWAW demo that may help.
I believe this pedal has the same controls as your pedal, but some of the names have been changed.
Resonance on SWAW = Q on Mooer
Bias on SWAW = Tone on Mooer
This video does a good job of describing the controls and demonstrating how they work. The SWAW sounds considerably different than MOOER, but maybe viewing the video will help you understand how the controls should work bit better.