Thank you both for your thoughts and kind words. A general update: the gastroenterologist advised my father to speak to someone in internal medicine, due to the fact that much of the pain now is located in his head. So we are now chasing that appointment!

Something else I ought to have mentioned: my father has been taking tocilizumbab (an immunosuppressant) for coming on 10 years now, for treatment of an (also mysterious and undiagnosed!) eye condition that was causing his eyesight to deteriorate rapidly. The tocilizumab has been successful in treating that condition, but it's strong stuff, and has given my father kidney stones previously. (We have confirmed that the abdominal part of the pain he is currently experiencing is definitely not a kidney stone!)

@loribmt

He has not been tested for Lyme's! However, he was given two courses of (different) antibiotics, neither of which helped. He also seems to lack a lot of the most common symptoms of Lyme's, such as fever, rash, and joint pain... Nevertheless, I'll add it to my list of possibilities!

@SusanEllen66

I think you're definitely onto something with a rheumatologist. Hopefully, the internal medicine folks, if we ever manage to get an appointment with them, will be able to shed some light on the matter. My thinking—completely uninformed and layperson as it is—is very much along the lines of inflammation or autoimmune; my sister has an autoimmune condition (lupus), which suggests to me there may be some genetic likelihood, and the best way my father can describe the pain he's experiencing is usually as an inflammation and tenderness. Which makes it even stranger that none of this is occurring in his joints, as you might expect, where he continues to experience no pain or stiffness whatsoever...