This is mainly a business problem since you can't have invoices that change their due date overtime.
You basically have an invoice posted in accounts receivable that has no due date until the customer receives the goods which may be after 2-3 days (or more).
That is unmanageable from an accounting point of view. I would be curious to know the stance of your audit team on the matter.
For these types of scenarios you should be probably use Proof of Delivery since what happens is that the customer doesn't accept a payment term that starts before he receives the goods, and that makes sense. In this scenario you bill after the customer confirms he received the goods.
Another dubious option is to block the automatic posting of the FI document document (very dubious, I don't recommend it). That way the SD document stays in VFX3 until the customer receives the goods, and you can use the base date as the creation date.