You are totally and completely missing the point.
That there are methods to "get it there on time" was not the issue at all. I grant that; NOT THE POINT.
The issue was a billing system, which in some cases, unnecessarily shortened the customer's payment window by a day, and which is preventable by "correct" programming. Program it so that if the computed day falls on a Sunday or a holiday, simply add one day (computers can do that pretty easy)--then check to see if THAT is a Sunday or a holiday; if so, repeat.