Stool Enzyme Testing
Bacteria testing based on stool is widespread, but unreliable. There is little known about the gut microbiome and how each bacterial species behaves inside it. It is just now being discovered.
Instead, a more concrete methodology would rely on established fecal tests for chymotrypsin, trypsin, and elastase (all used to break down protein) to detect any odor causing enzymes in the stool.
I have not looked into it yet, but the enzymes would be the ones related to odor such as methane-producing, sulfur-compound producing, toluene-producing, etc. The gas made in the gut should be a gas that somehow causes constipation for the host and gets across the gut into the blood.
It seems the established methods use antibodies, but a baseline would need to be measured from "normal" people to see how much of a particular enzyme they have, to see what is considered "normal." This could take decades, but its worth studying.
As for methane, which is shown to slow down the gut (causing constipation), a substance of note is bromoform, used in the cattle industry to prevent cow methane. It is toxic to humans, but I am sure a suitable dose or delivery method (perhaps directly to the colon via rectum) will come soon. Or other substances exist to prevent methane in the human gut. Ask AI for more.
Further, a SIBO test might not detect this mechanism. SIBO relies on the methane gases climbing up through the stomach. In this case, methane is contained in the colon, but the secondary effect being bodily toxins unable to leave and hence being emitted from us due to constipation preventing toxins from leaving quickly. This is compounded by most SIBO tests requiring you to fast beforehand, preventing colonic effects from being shown.