(I also have the opposite problem when the customers actually pay, because they often batch many invoices together into one payment, which makes reconciliation surprisingly difficult. I wrote a little script in Python to make that easier - sort of along the lines of "Given this total, which of these invoices could potentially satisfy it?" - but it's still frustrating.)
If the business continues to grow, I anticipate hiring someone to take care of this aspect for me in its entirety, because it's demonstrably a poor usage of my time, and I derive zero pleasure from it.