This is as close to: "Which came first, the chicken or the egg?" as you can get with BSA.
The customer reports $4,000 in cash Monday through Thursday. If you report on the customer's business day, no CTR. Yet the armored car delivers $16,000 in cash on Friday and it goes unreported? I would do the calculation on the bank's business day, not the customer's.
Yet, I would be uncomfortable not aggregating Tuesday's $4,000 cash deposit with a $7,000 loan payment or a currency exchange. However, I think it highly unlikely that a customer using this mechanism would have other cash transactions - it simply would not make sense.
Any vendor peddling this product/service, should ask FinCEN for an administrative ruling so they could tell their clients what to do with some assurance...
P.S. I assume any bank that would go along with this would require the customer to maintain a pledged account for the maximum possible amount of credit for as yet undelivered cash.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.