From the previous HN discussion, 00c for pawn and xxxc for other pieces is probably the optimal way to encode pieces into whole bits. Because you can sacrifice 1 pawn to enable 3 promotions, so you need to handle up to 28 non-pawns. With 2/5 you start at 14 bytes but can need up to 17.5. With 3/4 you start at 14 bytes and never need more than 14.

With 6 xxx states instead of 8, you can merge "king not moved", "rook not moved", and "en passant pawn" into a single state since those can never overlap. (Though if you're encoding one pawn the long way that means you need 14.125 bytes, oh well.)