A standard deck box for the big cards will work for the mini cards, especially with sleeves. Just turn the mini cards sideways and they fit! Problem solved! At least until "they" figure out a mini deck box that works better.
Edit:
If you only have a small amount of the mini cards, then you can fit them in sideways and standing up. I have way too many, so I lay them facedown and stack them. Getting them out isn't exactly fun, but I was thinking about glueing the lid shut and cutting the box in half to make it more like what we would need.
Edited by Sprolly G