Trouble finding plastic storage bins for MOCs built on 48x48 stud (gray) baseplates - Ideas?
The two solutions I've seen are to measure the size you want and visit places that sell a variety of storage bins so you can find one the right size. In Australia we have a variety of bins about the size of a milk crate or beer crate (about 12" by 9", from back in the day when those units were relevant). The modern plastic equivalents with solid walls and floor will hold a 48 square baseplate quite well, and are designed to stack.

A search for plastic storage container canada suggests that there are chain stores in Canada that sell things like this.

The other solution is to make (or have made) some wooden boxes. A woodworker will be able to cut 6mm or 9mm plywood up and make whatever size box you want and reinforce them a little so they can be stacked. Then you buy chunks of foam and cut them to suit your models. Or just make "bricks" in a range of sizes to pack around random models. The advantage of this is that you get boxes exactly the right size for your models. Using cut to shape foam rather than foam peanuts means that any small parts that fall off are easier to find. 

When putting multiple models in one container I prefer to put each in a plastic bag, again so that any parts that come off are easy to find and are associated with a specific model. Opening a big box with several models in it and finding a layer of small parts in the bottom is disheartening not to mention tedious to fix.