Gregor,
this sounds like a good fit for a custom implementation of the payment service contract. The custom payment gateway would place the requests for credit card authorization in a queue. The gateway returns 'failure-retry' so that the eCommerce package will accept the order and silently retry to authorize the card at a later time.
There is a parameter in the eCommerce package to specify how long the eCommerce should be retrying for. The default is 8 hours but you could extend that to 48 hours to give the finance department more time to perform the real check. Upon the first retry by the eCommerce package after the real check has been performed the gateway would return 'success' or 'failure'.
As the order is shipped the eCommerce package contacts the gateway to charge the authorized card. Again the gateway places the request in a queue for the finance department and returns 'failure-retry' and the request is handled in the same manner as the authorize request.
There is no need to change the logic in the eCommerce package. All customization is handled by the payment gateway.
/Bart