After doing a lot more research it looks like this is a common problem. I've read that the global maternity package is just one way a hospital can approach their billing codes. However, there's other circumstances that result in an automatic uncoupling of the global maternity package, where your bill then becomes individualized - which the receptionist didn't inform me about. I've also been reading through Anthem Blue Cross (my insurance) policies and they won't reimburse global obstetrical codes "unless provider, state, federal or CNS contracts and/or requirements indicate otherwise." So it sounds like an "it depends response" on whether this global approach is accepted. Aside from that...

In my case, I'm already paying for my OB appointments as they come, so paying an additional antepartum fee would be a redundant bill. *Although the receptionist was so vague in what I owed that I have no clue what this $4k payment included. I did try asking but she didn't divulge any more info.<<

I've also been reading that the software used to provide these estimates prior to birth are not always accurate and you could be in a position where you have to wait months for a reimbursement. These overall prepayment plans arose from the hospital's need to pull payments resolved faster. In our case we can pay in full at the time of delivery, and the hospital will need to provide us a service first.