Okay, so here’s something else that will be “harsh to read”. While I admit to not knowing what your surgery is about (and I’m not dismissing your need to have it done), it however doesn’t sound like a sudden issue of life and death to me, considering it is scheduled to take place a couple of months away. I think it is a matter of you determining which of these issues (scheduled surgery and potential interview date around the same time) means more to you. Seems to me like you have more control over when the surgery happens than trying to reschedule your interview appointment (again assuming interview gets scheduled around the same time.
Immigration/consular officers are human beings also, they can be quite accommodating when it comes to it as a matter of fact. Let me tell you about two DV cases with sudden personal medical conflicts to illustrate this:
About 3 or 4 FYs ago, a selectee processing AOS was suddenly diagnosed with some aggressive form of cancer while waiting to be scheduled for their interview. They were immediately hospitalized for a while, a couple of days before they got discharged and confined to their home, their interview got scheduled but they obviously will not be able to attend it because of their condition. They contacted USCIS to cancel the interview altogether to enable them focus on their health. Guess what, their IO visited them at home to conduct the interview and subsequently approved their application.
The 2nd story is CP related, it happened around 2008/2009. Primary selectee suddenly went into labor the night before their interview date. She delivered the baby about 5 hours before the interview appointment, the delivery was complicated, and she lost a lot of blood in the process, meanwhile the hospital was about 1 hour away from the embassy. As soon as she had the baby, she insisted on being temporarily discharged in order for her and her husband to attend the interview as scheduled. She had to sign a waiver in order for the doctor to temporarily release her. She attended the interview with the drip and transfusion lines still attached to her hand. The CO was beyond impressed when he saw her and her husband, which led to their being attended to promptly in order for her to return back to the hospital, the CO could see she was still in a lot of pain. The rest is history anyways.
Again, just saying there’s always a way around some of these things, if one looks really closely at the options and alternatives that they have.