Aha. You have to drag the slab to the small tab where it says "Sell" and not the basket. I knew I was missing something. I would definitely turn that entire zone into a sell region just to make that interaction easier to find.
If levelling up packs does change the drop rate, maybe there's a bug that prevents the game from showing that to the player? Here's a couple pics from when you mouse over the packs of different levels, and they show identical drop rates.
Thanks for taking the time to respond, and best of luck going forward!