Cardboard would be fine too. If possible cover some of the sides but the bottom is the main issue. The only reason I recommend feed bags is because it's an easy way to reuse them and I don't feel bad at all if I need to toss one that's soiled, and for a hard bottomed nest box (wood) it provides extra padding for eggs as well, all for free.
I do use wood shavings (aspen) in the nest boxes. I'm out of shavings now so probably switching to hemp after this as I don't use shavings for anything else.
Oh and as for the measurements, anything shorter than 12" between the two and I'd say it's too short for standard birds.