To date there has been no direct detection of gravitational waves by either method.
The bacteria exist in the body in relatively low numbers, making even direct detection difficult.
Recovery of the modulating signal is usually by direct detection, not heterodyning.
And I don't see how such an organization could escape direct detection.
This would constitute the first direct detection of gravitational radiation.
Long-term astrometry or direct detection could solve this problem, but no attempt to do so has yet appeared in literature.
At some point they should become so intense that direct detection by their effect on objects on Earth or in space is possible.
This direct detection is the goal of several large scale experiments.
Any such direct detection is complicated by the extraordinarily small effect the waves would produce on a detector.
In any case, direct detection of such a moon would be extremely challenging.