https://en.wikipedia.org/wiki/Lactobacillus_acidophilus
You got me off on a research project, lol.
So I got thinking and wandering - sprouting grains, bad smells, bacteria, and stumbled upon BREWERS forums,
Lactobacillus is a typically beneficial bacteria that produces sulfur as a waste product. It's build up and the excretion of its by products, sulfuric gasses, is a large part of what causes human and animal waste to smell. Poo smell, not typically present when just green waste or brown waste - composts are breaking down. Present when grains are breaking down.
If you were brewing, it would be what causes "sours" or what makes sourdough bread go sour. It's also airborne as well as water or mold, so it's not like you can sanitize the air.
The water is naturally going to attract them and even draw them out of "thin air" where they are overpopulating because there's nothing eating them and there's no way to get rid of 110% of them. For a second more of random wandering, winemakers use sulfur dioxide to inhibit it. Not helpful here, but interesting. Sulfa drugs... bacteria... makes sense. Something new every day... haha.
It likes low PH, so you could limit its growth by raising the PH of your water. If you have hard water, this may be why you're seeing such a fast build up. Calcium lowers PH. I don't know if you could use aquarium PH up drops to change the PH of the water you're sprouting with, and still have the end product be usable. I don't know if you could add lemon or vinegar to your water without it impacting the end product, but raising the PH of your water would slow the growth of the lactobacillus... There are types of algae and aquarium plants that also raise PH that maybe you could grow in your tank. Add fish for nitrogen.. lol.
It sounds like this might be your stinky bad guy. Interestingly, other sites mention that it can be cultivated with water that grains have been rinsed with, to make a solution of the bacteria for use in things like lactose intolerance and digestive imbalances, kind of supporting that as well, and how funny it is that in one scenario, it's a good thing, in another, it's totally not.
You have been successful at farming lactobacillus, without even trying! Which apparently some people work very hard to do. Lol!
Interested in how it goes for you, may try it myself, (the sprouts, not the acidophilus ;-) ) since the area around the hay pile sprouts every time it rains.