Is there a best time during the billing cycle to upgrade?

No, it doesn’t matter. There is no best time. Regardless of when you upgrade, the upgrade fee and installment plan will be on the next bill. By next bill, I mean the next bill cycle. If you upgrade in the fist 3-4 days of a bill cycle, you haven’t gotten the bill for that bill cycle yet so even though that would be your next bill, the upgrade charges won’t be there, they’ll be on the next bill cycle.