Talk of inducing

I had a drs appointment today (28 weeks) and my OB says she has good news and bad news. She informs me that she’s leaving the hospital and her last day is August 2nd...I’m due the 14th. The “good news” is that she is on call for delivery the last weekend in July. Because I’ve been measuring ahead the whole time she said we could “work something out” and that “he’ll be perfectly fine to come out at the 37/38 week range.” So what do you ladies think? This is my first and I have no idea what to do. Should I transfer drs at the final countdown and deliver with someone I don’t know? Or should I take the induction since he’s measuring ahead? Any advice or input is greatly appreciated.