I've always only ever bought mine after autocharge (ie, since Choice/Autocharge became a thing), and I don't recall ever having to reveal the keys (so it definitely should be possible to do). I think if you just click "Resume Now" on the main page (top right corner of the box with the icons of the included games) it works fine?

As Shakti said, the level 8 chance at this is appreciated. :)

Yep, like Sooth says, you just click on Resume Now and it should automatically bill you for this month.
You don't need to reveal the keys immediately but it's better to do so in case they run out of keys for one game.
If you buy the bundle in the next 5h you will still get the August Choice, otherwise your subscription will be resumed anyway once the September Choice is released.