AAAA rechargeables?

[Mr Happy]

I'm guessing they are containers that held two button cells in parallel then stacked in the fashion shown, but I dunno

No, I doubt it. If you look at the construction of NiMH cells they consist of a multilayer sandwich. In cylindrical cells the sandwich is wound in a spiral around the center, but in prismatic (square) cells the sandwich is just kept flat.

 

[Fallingwater]

Anyone ever taken apart a LSD 9V battery? What's inside?
Tiny cells would be useful for small projects, but self-discharge tends to kill them very quickly indeed.

Edit: actually, anyone knows a place where I could get one so I can do this myself? (as usual, I can't order from US-only sites...)