This is honestly how I would handle this problem.

Start with the biggest city that is ISIS controlled (dont care if it's Baghdad or what). Send in flyers. "3 days from now, every structure in this city will be destroyed, leaving behind only pebbles. Any person still in the city when this happens is considered an enemy. Thank you".

I swear I dont care if literally every single person good or bad leaves the towns. in fact, zero casualties (at this stage) would probably benefit us in the eyes of the "world". In fact, I might even support leaving 50 buses in the middle of town with the keys in em.. "get the fuck outta here guys". then you literally reduce the city into a pile of rubble. During this process, 24 hour drone patrols. all day, every day, drones flying low over their heads. tracking movement, obviously armed. somebody does something stupid, blow em up. equip the drones with a loud speaker message on repeat, saying that every person still in this part of the world is considered an enemy. la la la.

day after leveling city, more flyers go out. the next city will be destroyed in 2 days. boom. next city will be destroyed tomorrow. next city will be destroyed this afternoon. all the while with the drones. never once does an American soldier set foot on the ground. Literally never once. mix in a random, "this city will burn down in 2 days" or whatever. Literally using fire, destroy them. Tell the world that everyone was evacuated, and that there was an ebola outbreak there, necessitating the use of fire.

On the outlying cities, once a day, during prayer (coincidence mind you) drones blow up an "empty" structure. The purpose of this, is the water torture thing. One random building that by all accounts is empty, just goes away. Dont care if it's a shed, or outhouse. hell, dont care if it's one of the buses we gave em. blow something up.

What this will do, is allow at least a shred of "look, we dont want to kill civilians, see what we did?" with the flyers. Basically this is our disclaimer. yes I understand that nobody would support this wholeheartedly on the worlds stage, but in the back rooms everybody knows what needs to be done. This will also show an amazing amount of power. we dont even have a to put a boot on the ground, and we will dominate you until the end of days... Once it comes time to go into "sovereign" countries, we give them the option of continuing our strategy. If they politely decline, tell them we will sell them Iraqi oil at half price for 50 years to be our ally, and let us help rid the world of this problem. "Sorry Turkey, but the only thing that will ever enter your airspace, is a missile every day or two coming from the gulf, until these bad guys leave you and yours alone to live prosperously. "Keep in mind Turkey, that although it's phrased like a question, it's not. Thank you".

This will force the bad guys to constantly be moving. Into the hills, etc. This will force the "good" ones, to be moving also. Some of them go here, some go there, whatever. (Yes I know what that could eventually lead to). I mean, literally, eventually destroying every single building in iraq, afghanistan etc. We reserve half the oil rights, (because look, we already got fuckin lambasted even when we didnt take oil the last time), and we restructure the entire region. No more iraq. no more afghanistan. Isreal, here's a chunk if you want it, Jordan, heres a chunk if you want it. UAE, heres some, go get rich homies. Think about a country like the UAE, taking truckloads of money in there, printing even more money when they finally set up shop, and pretty soon, the country formally known as iraq will be the biggest tourist destination in the world. oh and not to mention, we are now making money selling oil back to the middle east. which we would invest in free cell phone programs and free health care here in the states so that the retards that we have here will even be on board with the plan.