Let me go ahead and apologize in advance for the long info/repeating any info you already know lol. I’ve just done a lot of DIY projects for my hamsters throughout the years.

The bin idea is a good idea for depth, the only concern would be ventilation. It is easy to get a buildup of ammonia and moisture in bin cages that are sitting on top of each other. You could always cut windows on the sides of the bin and add hardware cloth for better ventilation. The downside is bedding/food may fall out as it gets moved around.

You could also just slit the ends of each bin, attach with zip ties, and build a tall wall/frame along the outer rim of the enclosure. This way, you could add more bedding and it would also count towards floor space. I’ve done it in several different ways, as it’s easy and cheap to make.

1 - I got unfinished wood slats from a craft store and measured it so that the finished wall would have a slight gap all around the bin cage. The gap should make the finished wall loose enough to start sliding to the floor. Then I used (non-toxic) hot glue to attach the wood pieces together and hot glued long dowel rods (horizontally) along the bottom inner part of the wall. (The dowel rods should be slightly wider than the gap.) The gap/dowels made it so that I could easily remove the wall during cage cleanings.

2 - I got moving boxes from a hardware store, cut it as high as I wanted and left a slight gap. I covered all of the inside walls with popsicle sticks and then added the dowel rods the same way I mentioned above. Then I applied a few coats of Mod Podge over it. The sealant hardens the cardboard/popsicle sticks and prevented my ham from chewing it. I honestly didn’t need a lid at all because of how tall the wall was, but you can always add the hardware cloth to the top and secure it with hot glue.

As for the bedding, making it as compact as possible will hold the best burrows. For me personally I like to mix orchard grass with the bedding because I think it holds better burrows than just layering.

Also what kind of hamster do you have? Wheel size is determined by the hamsters posture while running. It should look the same as if they’re running on the ground. If it’s a dwarf a 9 inch wheel should be fine but it’s possible they might outgrow it. My girl is a winter white and she’s tiny but can turn herself into a liquid pancake. I had to upgrade her to a 10” wheel that had a wide running track. If it’s a syrian I’d recommend a 11” or 12” wheel. I also would avoid using sand paper lining in wheels. Hams run a lot and could start filing down their feet. You could instead add sandpaper to a tube/platform, use rough rocks/slate (found in the aquarium section), or bricks from a hardware store. You’d just want to place them near an area they’ll frequently visit, like where their water is.