FedEx Delivery Dates are off

In checkout, FedEx displays a delivery date which is correct early in the day, but incorrect in the evening / late afternoon.

Here is the FedEx delivery info in checkout:

But ... it says it will deliver on November 9, whether the customer places their order at 10am on the 7th, or 11:59pm on the 7th.  

Even if we were shipping orders 24 hours a day, FedEx isn't going to pick the order up at 11:59pm, so really, orders placed after a certain cutoff time (perhaps 2pm) should say they will be delivered Monday, November 12.

Is there / can there be an option to set our shipping cutoff, and have it affect this?

Or have a default of noon or 2pm?

Or simply remove that precise date and go back to the way it used to be -- which just said something like "2 days".

It seems like this API must have affected more people than us.  It has really made a few customers angry at us recently, because they believe the date they read.

I do see this in Admin -- but we don't actually need a full day delay.  If you place your order in the morning (or by 2pm most days), we will ship it same day.  But if you place it at 10pm, FedEx is closed, so it wouldn't even matter if we were open!