"If they want to be seen, they have to pay at least part of their balance and we roll on from there."
This tact can work, but it can also backfire. You see, they don't have to pay anything to be seen, and some of them know this, especially delinquent type people. You cannot refuse service or you are abandoning them. Also, if you say you have to pay to be seen, they can go online and say they were sick and you refused to pay without extorting more money for their illness. It's not pretty.
People who don't value your time... people who would rather pay a cell phone bill than you... people who buy cigarettes over paying you... do you really want these people in your practice?