Your topic title is not really correct, Urease positive ie ammonia producing micro-organisms can occupy many different places in humans and not just the intestines. They can be present in the urinary track, mouth, stomach to name a few places.
I think that you should look at the most likely places, where the most ammonia will be produced. This will be where there is an ample supply of urea which the Urease enzyme will turn into ammonia and carbon dioxide. Ammonia is quite highly base which can neutralise acid. Couple that with the stomach and this can result in hypochlorhydria and gas. An acid challenge test might indicate their presence by producing wind/burp. Ammonia carbonate can be formed which
might not cause so much gas and therefore it might not be so easily detectable by such a simple test. An acid challenge does show burping in me. This may or may not be the micro-organism which causes CFS depending on it's location, it could be merely a co-infection.
Staphylococcus spp. can be Urease positive and so can Nocardia spp.
Staphylococcus aureus, Enterobacter cloacae, Citrobacter freundii, Ochrobactrum intermedium, Proteus mirabilis, Klebsiella pneumoniae, Helicobacter pylori, Proteus vulgaris, Ureaplasma urealyticum & Staphylococcus capitis subsp. ureolyticus, Cryptococcus neoformans & Cryptococcus gattii to name a few.
A note:
Histamine which is needed to stimulate stomach acid production also causes vasodilation
Urease-positive bacteria other than Helicobacter pylori in human gastric juice and mucosa Brandi et al 2006
Urease-positive bacteria in the stomach induce a false-positive reaction in a urea breath test for diagnosis of Helicobacter pylori infection Osaki et al 2008
If you search for Urease bacteria, yeasts, fungi, microorganisms then you should turn up a great deal of results.