First I found a clever way to minimize the amount of bits necessary to describe a board position. I think I hit 34 bytes per position or so, and I guess further optimization was possible.

Indeed, using a very straightforward Huffman encoding (1 bit for an for empty cell, 3 bits for pawns) you can get it down to 24 bytes for the board alone. Was an interesting puzzle.

Looking up "prior art" on the subject, you also need 2 bytes for things like "may castle", and other more obscure rules.

There's further optimizations you can do, but they are mostly for the average case, not the worst case.