(Former) pawns can be on the 1st or 8th rank if they've been promoted. You can place an unpromoted pawn on the 1st or 8th rank to encode en passant, too.

Also castling can be encoded as extra squares available to the rooks only ("queen side never moved" and "king side never moved"), and that is almost free.

But without a good encoding for promotions, I doubt you can beat the encoding of the article.