Yeah, I know you said you wouldn't be traveling but I thought the net $405 SUB was higher than what you're looking at with the BCP or BCE for a $3K bill. The other thing you want to be sure about before getting an Amex, is that the hospital accepts Amex. I've been surprised sometimes by places that don't. The BoA Premium Reward card is a Visa.
BoA definitely has its ups and downs, but then so does Amex. Since everybody's situation is different, I can't really say if they're hard to get approved for, I know some folks on this thread have had success and some have had failures. I've read they are a relationship bank, so they want to see you have some account with them and that improves your odds. But then some have gotten approved with no relationship so who really knows?
Good luck deciding!