So here's my first crack at a 44-square chess variant. The black space in the middle is a non-space, a hole in the board. The red squares are some sort of funky translocation squares, I'm still working out the details.
The pawns are berolina pawns, the kind sort of inverse to regular pawns, they capture forward and move diagonally. The upside-down rook is a Crook, which moves like a rook but also has a one-shot knight movement. After making the knight movement the Crook is flipped back over to show it is a regular Rook for the rest of the game. The bishops can also move one square orthogonally, making them dragon horses, popes, or ladies depending on the source of your terminology. I was going to use standard bishops until I realized all four were on the same color squares.
No name for this variant yet. Based just upon the pieces "Crooks & Popes" might fit the bill, though it sounds potentially anti-Catholic. The board should really figure into the name, since its a board-related contest.
If I get this puppy submitted, maybe I'll do a Crook page for the Chess Variants Piececlopedia. And I still need to seriously tackle an Enochian Chess page for the site.