A credit balance will report as a zero balance.
General drift on the forums is that the highest score results from two or three national / bank credit cards. "Less than half" but at least one reporting a balance, and rotate which ones report a balance each month. Keep utilization below 10%.
I remember one post where the OP did what you're doing, took all to zero balance, then let one card report a small balance and the score went up slightly.
