You have to understand that the freezing of the card is computerized. It's not like there's some guy going through all of the accounts with a clock next to him salivating at the prospect of cutting off your charging ability when you go one second over.

While empathize with your situation in Houston, you should know that you need to make a payment to satisfy the Minimum Payment for a billing cycle. Even having auto-pay set up for the minimum amount each month only takes seconds of your time on the website. There is absolutely no downside to it either since the auto-pay won't trigger if you made another payment during that cycle that satisfies the minimum amount due.