"What if the over-payment was in a previous closed month, ie: January 2017,"
Then you were carrying meaningless Negative AR all this time?
"and the customer short-paid the amount of the over-payment on their next payment in February?"
Apply their payment now.
"How do I use that over-payment towards the short-pay without disrupting the closed month of January?"
You already have the money. It is time to apply it.