Quite a few redemptions I make to the US tend to be on "later in the day flights" i.e. ones arriving 8pm onwards and this would fit in with an off-peak period.
That said, it's not always the case that there isn't availability throughout the day but most of the time, the off peak flights are easier to pick up.
If I was just going to pay straight cash, I would fly as cheap as possible and earlier to maximise the time at my destination.