The easiest solution I have for you is to stop running this in-house. Your staff has so many other tasks to deal with that they are probably exhausted chasing up patients trying to get money. This is how things like billing mistakes happen in the first place; the best thing a US medical practice can do is hire a medical billing service.

Hiring a service to do this for you is more likely to ensure that people pay up when they should. This allows your in-house admin team to focus on other aspects of their job without having to chase up non-payers. You should be able to find a local service that can do this for you; I recommend looking into Healthcare Billing Services, which has helped out lots of companies in the exact position you are in moving forward.

Trust me, having a third party manage your billing just makes your day-to-day life so much easier and allows your staff to focus their attention elsewhere.