Keep in mind that "responsible usage" is defined as keeping balances under 28.9% of limits. And paying your statement balances in full by the due date will avoid any interest.
That said, AZEO (all zero except one) will optimize your scores. That's where you allow a tiny balance on one card to report with the rest of your cards reporting zero. You may wish to aim for this at times when you're applying for important credit, if you wish to use the numbers while testing your score, or if your score is on the low end.
I like using AZEO when I'm testing scoring behavior. I recently tested to see what happened when a single balance went from $6 (AZEO) to $896 to $1425. Keeping only the single balance kept other factors from muddying the results. Another test involved two very low balances compared to AZEO.
For the most part, I think that keeping all cards at 28.9% or below is sufficient. If you're applying for a mortgage, you should be prepared to do AZEO if it'll get you a better rate. I'd also suggest AZEO or something close to AZEO if your scores are such that you can bump yourself in a range that's desirable vs. undesirable, like bumping yourself over 680 or 700. And testing one's scores and becoming familiar with how they react to (reasonable) reporting behaviors is always cool.
The only way to control balances at reporting time is to curtail the use of that card. That usually means a couple of days where you stop charging entirely or keep your charges low enough to stay below your desired balance. The workaround would be to use a different card during those days.
As you get better at this, you'll be able to cut things pretty close. You want to your pending charges and your payment to clear by the day before the statement cut date. Check your statements for merchants you use routinely. If you see that they claim their charges quickly, you can charge almost up to the last minute. If you know a merchant tends to dawdle in claiming pending charges or you've never shopped with a merchant, allow more time for charges to clear.
You have extra leeway with Chase and Discover. In addition to reporting the statement balance, Chase reports zero whenever you pay to zero. And both cards will report your balance whenever you call and ask them to.
