Just read all this to get caught up. It seems to me that it's time to get a second opinion. Unfortunately medical care in this country sucks, so you need to do some of your own leg work.
I'd find another gastrointerologist and also an infectious disease specialist. Post op infections are common, but need to be addressed properly.
Diverticulitis is a common gastro surgery with a very high survivability rate.
Regarding the dimentia you mentioned due to meds, it is called "sun downing" and although very upsetting, it is highly common and not a specific cause of concern for the patient other than mental anguish.
The bottom line is (without being aware of situation) the doctors need to figure out why her WBC is low before they administer any more antibiotics.
At this point since it has been months, she needs to be rescreened for cancer given the WBC. It is possible that the doctors missed a cancerous polyp in the bowel. She should also be screened for bone infection, and leukemia.
Again it is possible they missed a polyp or botched the test, but highly unlikely. It is far more likely that her immune system is reacting to the infection, and the docs just need a bit more time to prescribe the proper antibiotic. It is actualy a good sign that they are waiting, because if things were critical they would throw strong antibiotics at it immediately instead. Take a deep breath, and think positive.
Best of luck & prayers,
-Freq