A few things:
1. If you were going for the AZEO, some lenders may not report a balance under $5 and you may be socked with a 0% util score penalty for that month
2. Any util less than 8.9% is generally counted the same
3. Both of my AmEx cards lets me prepay my balance even when the posted balance is $0 and the transaction is still pending. If you are that worried about it, you can give it a try.
Honestly, this is not a problem. These days I'm having to deliberately tell myself to not pay some balances before statements cut just so that I'd have a few non-zero balances.
