I think baltic birch holds up much better than other plywoods to tearout. And I agree, the look is nice. Actually that picture I posted does not really show how good it can look. I was just at the mall last night and noticed a table made from BB ply with oversized dovetails. It was a modern and interesting look.
Baltic Birch is imported from both Russia and Finnland. The products coming from each country are pretty similar. Both come in 5' x 5' sheets, which I actually prefer to the typical 4x8. You will need to look for these products at hardwood specialty stores most likely.
You can buy cutoffs in various sizes at Bargain Birch Dot Com. You may have to check often to get the widths you need for your boxes. But last time I checked the price was cheaper per square foot, even once you factor in shipping.
I don't know if you have Menards in your area, but they carry a BB knockoff that comes in 4x8 sheets. It is decent stuff but there are some delamination issues and I think you would experience some tearout.
There is another product called Appleply that has a strong distribution in the southeast United States so you might be able to find it in Florida. They also make drawer stock which is precut into panels so you may find some of those that will work. Appleply is a premium product.
Lastly, Columbia Forest Products makes a really nice plywood called Europly. It is the most expensive but nicest looking of the high-ply plywoods. Actually aircraft plywood is more expensive but that's hard to find so I won't even include that.
Europly also comes with an ultra-violet cured epoxy coating on both faces. Europly also has the nicest grain of any of them on the faces.
I do remember the thread from Thanksgiving and think you've outdone yourself. I think these boxes made from some sort of high-ply plywood and the DANGER drilled in the sides could be popular. Back when I kept venomous I would have bought one, even though I already had a few modified tool boxes that I used.
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Currently keeping:
6.10 Gonyosoma oxycephalum (Javan, mixed colors)
0.0.4 Rhynchophis boulengeri
1.1 Philodryas baroni
1.1 Lampropeltis triangulum multistriata
0.0.1 Rhamphiophis rubropunctatus
0.0.1 Morelia viridis "Aru"
0.0.1 Morelia viridis "Merauke"
1.0 Rhodesian Ridgeback