Unless it's a life and death situation, why do you want to complicate life? As many data points suggest, if she applies for expedited passport, she should get it within few weeks here in the US.
If it is an emergency, maybe it makes sense postponing oath and travelling on GC, unless you think the trip will be long?
Follow the standard process to ensure smooth travel. Deviate from it - and you will either pay more, wait longer or both.