Wouldn't "Corruption Not Allowed" and "Into the Trash" be a better combo for this? It'd give three equipment capacity and also reduce corruption as an additional small bonus. And using your math for the cost, 19.16/0.1375 = 139 green gem cost for "Corruption Not Allowed" and 19.16/0.055 = 347 green gem cost.
139 + 347 = 486 average cost for the two cards, which is less than double the cost of "Backpack Check" for an additional equipment slot. I agree that Backpack Check is weirdly powerful, but I think that more powerful strategies exist if you look at the farther down packs, especially using "Corruption Not Allowed" to compensate for the additional corruption.