Interesting question. IMO, the humiliation should be a maximum, the person should be fully aware they have no other option but to poo, but the mess should be kept to a minimum. Stinky poo everywhere is not a good look, IMO.
This is what I've done. The recipient must get fully undressed. Absolutely nothing left on. A soft pad is put on a table, about 3' x 6', and the receiver has to bend over and rest their torso on the pad. Their feet are wide spread and ankles attached to the table legs with soft Velcro straps. Another Velcro strap goes around their body, under their armpits and holds them to the table. If desired, their wrists can also be fastened to the other table legs. The person is completely exposed, not uncomfortable, but completely helpless and all their private parts fully exposed.
A folding camping potty, with disposable poo bag, is then placed between their legs under their butt, and they are invited to poo. It is possible some may be successful and every detail is fully exposed to view. But, if there are no results, they can be encouraged with a few paddle swats. If still nothing happens and/or they resist pooing, a Magic Bullet suppository or a small enema of a few ounces of glycerin is given, and results are awaited. Of course, you never tell what you put up their butt, so they have absolutely no idea what to expect. Even the most reticent will poo within a half hour and their humiliation will be intense intense. The more they resist, the more effective the treatment. When they are done, the position is perfect for the further humiliation of having their butt wiped and washed. A further touch is the insertion of a Preparation H suppository, following a dose of the ointment.
Cleanup is easy... just tie and toss the camping toilet poo bag.