Just use the card
Utilization DOES play a part in your FICO score. What hurt your Fico score is carrying a balance of more than 35% of you limit (i.e. 35% credit utilization).
Even if your score takes a hit because of high credit utilization, it will immediately rebounds when you pay it off.
It really doesn’t worth the efforts to try and determine exactly when your card updates the credit bureaus and then try to schedule your payments to create a perfect utilization rate.
Just use the credit regularly as you need, pay off the balance in full and your score will be fine. It really makes no difference how much of your line of credit you use if you pay that balance in full every month. It all evens out in the end.
In fact, the fastest way to get your limit increased is to use 70%+ of your limit and pay the balance in full every month for about 9 months.