That's very calm, and it's perfect. As someone who works in a roundabout way for a hospital, they honestly MAY feel it's too risky. However, if they do, what they're supposed to do is tell you so and then let you find another hospital. Not string you along. That's just.....GAH. I'd ask politely and repeatedly if the doctor is uncomfortable performing the surgery. Have it be your Toots Special. If they finally say yes (I suspect they might), then you can begin the transfer.
Best of luck. And *HUGS*