there are a few people who use large bins like yours...your commercial stacking bins would probably be the best but they are pricy. I have made myself a stacking system with meat / fish crates which works quite well. They are a little deep but work quite well. Have you thought of a flow through bin. Easy harvesting is a major advantage with this bin. Hope this helps.

Rubbermaid makes a 10-gallon bin, which would be just what you are looking for. It's not as easy to find in the stores as the larger sizes, though. Lowe's has it on line, and I think some though not all of the Lowe's stores have it in stock.
The rubbermaid 10-gal is called for in the directions for the OSCR Jr. stacking bin system. The plans are on line.
mbetts

To get more surface area rather than depth, I use the under-the-bed containers. These are about 7 inches deep, 18 inches wide, and 4 feet long. LOTS of space in that. The drawback is that they are not nearly as portable as my traditional bins are.

You need to use a tote by Rubbermaid called Roughneck. It is wide and shallow with straight sides.

The one I really want is the one this woman uses in this youtube video link down below...

Here is a link that might be useful: Video link

Looks like a kitty litter pan to me.
mbetts

takadi -- The container in the video looks like either a dishpan or kitty litter pan. Both are relatively inexpensive. You might also try emailing the maker of the video for clarification.

Cool, can you find these at walmart or something? I'm hoping I can still fit the lid of my 18 gallon rubbermaid over a kitty litter pan.

I'm hoping to recreate the Wriggly Wranch stacking system using much much cheaper bins

Back in January this year when Lowe's and Walmart were closing out their Christmas decorations they both had a deep discount sale on bins to put the decorations in. If you still have a need check next just after Christmas.