So, uh...
It's cardboard. Just do this fot every drop maybe? If you want to know what artificial scarcity does, just look at the Pokemon TCG.
It's really not that complicated. If you can do it once, there's very little reason you couldn't do it every time. In your order window (24h, 48h, whatever) you collect all the orders, then use that quantity to inform your printers so they can print off the exact quantity you need. You get the bulk discount still, you avoid printing unnecessary cards (ignoring refunds/cancellations/extra stock for misprints/whatever), and everyone who wants it gets it. After the order window? You get your scarcity too.