Long term I can see Rome trying to take and integrate the Mosul area. With that firmly in Roman hands the Roman heartland and Levant are secure while the heart of Ottoman power is now on the frontier.
It would be tough to take and it would require population “transfers” to put it mildly to hold onto but it would effectively neuter the Eastern threat for good.
Call the Arletian slave merchants and tell them you have more "product" for them to sell off.
Wait so the Romans are basically going on a death march against it Muslim populations at home becasue of the constant rebellions and massive losses life, money, soldiers, etc. So due to the fact that just wiping out the entire population is costly and would prob have a physiological impact on them as well. Prob cost some money as well. Why not move these pop to the Ottoman empire destabilize it a bit and foreign populations and stuff concentrate the ethnic groups so that they are they go to becomes the majority that and cause the empire to further fracture and weaken the ethnic groups. This would cost money but the other options is to move them to the European side of the empire and just cause chaos in the enemy empires? Too cRazy
Why give your lifelong enemy more manpower to (possibly) use against you in a future war?