1 person in 5 was a slave in the Ottoman Empire in 1900, and the Empire itself spanned hundreds of thousands of square kilometers, from Algiers on the Mediterranean through to the Caucasus in Asia.  If you think that the administration of an Empire that large, run almost completely on slave labour, didn't involve mass movement of slaves to where labour was needed, and that this didn't often involve significant injury and death, you're fooling yourself.

Makes me laugh, though, that you're truly seeking to split hairs and argue on who was really a worse practitioner of slavery. Once we've established that they owned people as property by the millions, and bought and sold them in Constantinople in huge lots at a pop, we've established their moral character, in my opinion.