Morphine would be an unusual choice for intractable diarrhea, and unusual choices make people nervous with narcotics, since the DEA is a nasty and merciless watchdog. The most "standard" opiate treatment for diarrhea that can't be controlled by Lomotil and symptom control measures (e.g. Metamucil to bulk and thicken the stool), as well as proper diagnosis and treatment of the cause, (such as pouchitis), is DTO (deodorized tincture of opium). It can be hard to find a doctor knowledgable enough to prescribe it, or a pharmacy brave enough to dispense it. It tastes awful. Paregoric is the same stuff in a much lower concentration.
I don't think you'd ever get a pain management doc to prescribe these, since they aren't particularly good for pain management. A good gastroenterologist *might* be cooperative, assuming you're willing to cooperate in exploring alternatives that might be better. Opium is kind of a last resort.