I’m in Seoul now, but in my early 20s, I had double-jaw surgery at ㄹㅈ Dental Clinic in Daegu. There was excessive bleeding during surgery, but they collaborated well with a nearby university hospital, so the surgery ended safely.
People around me say my face became much smaller, but I do think I wish it were a bit more slender. After surgery, I heard from the doctor that if they made it more slender, side effects might occur, so they cut an appropriate amount.
Of course there are many hospitals in Seoul that are good at double-jaw surgery, but if you plan to have it done in Daegu, I recommend that clinic. I think you’ll be able to receive double-jaw surgery safely above all else.