Are there any boxes that a Card Saver I (the bigger one) would fit in? So the top of the box fits

I assume you mean a cardboard box. Yes, they make a 2 row box that’s tall enough for CS’s and graded slabs.

@backbidder said:
I use this -

BCW Graded Card Shoe Storage Box 2 Row

Me too, or the boxes PSA returns cards in for smaller quantity.