Has anyone had experience with a patient being obsessed with bowel movements to the point of sticking things in their rectum to "dig it out"?

This is in fact extremely COMMON in elders. The longer feces remains in the lower bowel the more fluid is removed from it and the harder it gets until in fact it is almost like cement. At that point the already slack and inefficient musculature cannot move the feces out. So question one (since you are there and can observe) are you seeing feces in the otherwise normal stool that is quite hard?
Some elders with no memory are well served with a chalk board in their bathroom with the day, date, and whether or not they had a bowel movement and whether or not it was a "good one".
It is quite unusual for this digging to go on without constipation.
It is never a good thing to do rectal stimulation in this manner unless trained and proficient at it, as rectal stimulation can actually trigger a general collapse with loss of consciousness.
I think that there must be some dementia involved if you cannot discuss this with you patient.
A nightly dose of a fiber supplement (I recommend citrucel over metamucil and the former doesn't ferment in the gut in a way that produces a lot of gas and subsequent explosive diarrhea) sometimes causes an elder to have an early daily BM that honestly doesn't leave a lot of time for this digging around. If the problem however is going on during the day it may be one of a much more compulsive-dementia habit. Just occ. small or low dose anti depressants work with such things if they can be tolerated; I would speak with the patients doctor if this continues.