Put your best foot forward; be soft-spoken, courteous, well-mannered, chivalrous, and respectful.
Given the fact that doctors, esp surgeons, have a very busy life in US, it seems logical. Everyone has their own sins and impure thoughts they need to overcome.
I look at my single male doctor colleagues and some of them are sweet and honestly looking for a connection. But from what you said, this girl doesn't sound like she is going to be content to have a marriage for time only.
If things get even more serious, try getting her to sign a pre-nup that neither she, nor her family will try to convert you.
She was a mormon and he finally joined the church at For 40 years there was a disconnect and she really viewed him as a lesser person cause he wasn't a member. Accept yourself, and feel God accepting you, and everything else will follow.