I like the cold turkey method (no pull-ups) for my own kids but not for group care. One option I know has worked for other is put a pull-up over their underwear. That way, no washing plastic pants (as was their concern), the child still gets the uncomfortable feeling of soiled underwear and you get the containment needed.

Just an aside- my daughter was born with bowel problems and needed corrective surgeries at birth and as an infant. I have learned a thing or two about poop through it all, heh heh. The specialists at Sick Kids have told me that often kids can have a hard time relaxing their sphincters and sitting on a regular toilet can make that harder (as their legs are lower). Sitting on a potty can help this as they are mor ein a "squatting position" and also takes away the splash factor.